Evaluation of a Random Sparse Sampling Design: An Assessment of Power and Bias Using Simulation

K. Kowalski (1), M. Hutmacher (2)
(1) Pfizer, Inc., Statistical Research Center, Ann Arbor, MI, USA; (2) Pfizer, Inc., Statistics, Skokie, IL, USA
oral presentation
Objectives: Assess power and sample size requirements for a population pharmacokinetic (PK) substudy of a phase III clinical trial using simulation.
Methods: A simulation study was conducted to determine the sample size (number of patients) that would achieve adequate power (i.e., >80%) to detect a 40% difference in oral drug clearance (CL) in a subpopulation of 5-10% of the total population. The simulations were based on a population PK model developed from phase I healthy volunteer data. The simulation model was a two-compartment model with first-order absorption. A sparse sampling design was proposed based on practical considerations and clinical convenience. It was anticipated that the sparse sampling design would not support fitting a two-compartment model. Thus, simulations were also conducted to assess bias in CL and the apparent steady-state volume of distribution (Vss) estimated from fitting a one-compartment model. The power and type I error rates for a likelihood ratio test on subpopulation differences in CL based on the one-compartment model were also assessed.
Results: The proposed design fitting a one-compartment model can provide accurate mean estimates of CL and Vss when the true underlying model is a two-compartment model. However, the size and power of the likelihood ratio test for subpopulation differences in CL are inflated when using the one-compartment model. The simulation results suggest that an approximate 9-point change in the objective function value corresponds to the 5% significance level rather than the commonly used c 2(1) critical value of 3.84.
Conclusions: In the presence of known model misspecification, likelihood ratio tests can be anti-conservative (inflated type I error rates) even when the analysis model provides a good fit and accurate estimates of the fixed effects (including covariate effects). Simulations can be used to assess whether sparse data can support fitting all the parameters of the assumed (simulation) model or whether a simpler (analysis) model may suffice. When a simpler (misspecified) model is considered for the analysis, simulations should be performed to assess bias in the key parameter estimates (e.g., covariate effects on CL). Furthermore, simulations should also be conducted under the null model (no covariate effects) to characterize the distribution of the likelihood ratio test as the type I error rates can be substantially inflated. Moreover, the power of the likelihood ratio test may also be inflated and can be adjusted based on the empirical distribution of the likelihood ratio test obtained from simulations under the null model.

Case Study in the Use of Bayesian Hierarchical Modeling and Simulation for Design and Analysis of a Clinical Trial

William R. Gillespie
Pharsight Corporation, 800 W. El Camino Real, Suite 200, Mountain View, CA 94040 USA
oral presentation
Objective: The objective of the work presented here is to optimize the design and analysis of a Phase II proof-of-concept (PoC) trial of a potentially disease-modifying drug for treatment of a slowly progressive illness. The trial design and analysis are to be optimized with respect to the quality of the PoC decision given limited prior information and consequent high uncertainty about the drug's effects. This is a case study illustrating the use of Bayesian principles and methods that provide a coherent framework for quantifying that uncertainty and for making inferences in its presence.
Methods: Bayesian methods are used consistently throughout a model-based approach. In particular they are used for model development, trial simulation and trial analysis. A hierarchical model is used to describe disease progression and efficacy response to drug treatment. The model is fit to prior longitudinal data using a MCMC method (WinBUGS). The resulting samples from the joint posterior distribution of the model parameters quantify the correlated uncertainties in those parameters. For the trial simulations uncertainty in the model parameters is considered by resampling from the posterior samples. Three approaches to trial analysis for PoC decision-making are applied to the simulated trial results: a conventional frequentist analysis of endpoint data (ANCOVA) vs Bayesian hierarchical modeling of longitudinal data with or without the use of prior data.
Results: The selected model describes the time course of log(efficacy score) as a linear decline over time. The effect of dose is modeled as a proportional change in the slope of that decline. Log(score) at the ith observation time in the jth patient is modeled as: 
log(scoreij) ~ N(aj+bjtonset,s2) 
aj = a0j+qsexImale+qage(age-55) 
bj = b0j+qdrugDose 
(a0j,b0j) ~ MVN((qa,qb),W) 
where tonset is the time from disease onset. Relatively diffuse priors were used for the parameters.
The performance of each trial design is measured by the probability of reaching the correct PoC decision, i.e., go for a "winner" drug and no-go for a "loser" drug. The working definition of a "winner" drug treatment for this disease is one that results in at least a 25% reduction in the population mean rate of decline of the efficacy score. For each simulated trial the "true" population mean drug effect is calculated from the model parameters (sampled from the previously estimated posteriors) used for the trial simulation and the drug is categorized as "winner" or "loser". The simulated trial is then analyzed and a go/no-go outcome is assigned. The idea is to choose a trial design and a go/no-go decision method that minimizes Pr(loser|go) (approximates probability of a Phase III or marketing failure) and Pr(stop|winner) (probability of a lost opportunity). A key conclusion is that the quality of the PoC decision for this drug and disease is markedly improved (relative to a conventional endpoint analysis) by using Bayesian modeling of the longitudinal trial data combined with relevant prior data.

Obesity and Insulin Resistance: A Fat Link

Katarina Jelic, Morten Colding-Jørgensen
Dept. of Scientific Computing, Novo Nordisk A/S, DK-2760 Maaloev
oral presentation
Goal: There is a growing need to understand the link between obesity and type 2 diabetes. An important link is between the fat tissue and the fate of the lipids in the body. To gain an insight in this, a mechanism-based mathematical model of lipid homeostasis has been developed. This type of modelling, called Biosimulation, allows a quantative examination of fatty acids (NEFA), ketones, and triglycerides (TG) and their movements. The model can facilitate a more efficient selection of drugs and drug targets in the hunt for new efficient treatments of type 2 diabetes and obesity. 
Method: The model is based on a set of differential equations for the metabolites. The physiological and biochemical relations and parameters are determined based on literature data. Delays are modelled as third-order delays. 
Results: It is found that the insulin level and the insulin sensitivity in adipose tissue is the main controller of the NEFA levels in plasma. After a meal, there is typically a suppression of NEFA levels in plasma, but the length and the degree of the suppression are highly dependent on the nutrient mixture and the energy content of the meal. The postprandial decrease in NEFA causes a drop in the fat oxidation rate, thus allowing glucose oxidation to occur. Changing the insulin sensitivity in the adipose tissue gives a change in the plasma NEFA level. This affects other tissue (primarily muscle and liver) both in the postabsorptive and the postprandial situation. Decreased insulin sensitivity in adipose tissue and an increased adipose mass, as seen in obese individuals, results in higher postabsorptive NEFA levels and higher NEFA fluxes to muscle and liver. This decreases the glucose oxidation and increases the hepatic NEFA reesterification. The model shows how a mismatch between insulin levels and adipose insulin sensitivity results in higher postprandial NEFA levels. This exposes extra-adipose tissues to excessive NEFA fluxes and leads to impaired postprandial glucose oxidation and lipid accumulation in other tissues. Weight loss in obese subjects causes a lowering of adipocyte insulin resistance together with a lowering of NEFA levels and NEFA oxidation. 
Conclusion: The fat link: Adipose tissue insulin resistance, as seen in obesity, leads to development of insulin resistance in muscle via the fatty acids and their fluxes in the blood. Alleviation of adipose tissue insulin sensitivity via weight loss or pharmacological treatment will result in lowered NEFA levels in the blood. This should improve whole-body glucose homeostasis both postabsorptively and postprandially. 

A pharmacodynamic model for Scandinavian Stroke Scale data

Fredrik Jonsson and Niclas Jonsson
Uppsala University, Sweden
oral presentation
Objectives: Stroke severity is commonly measured on aggregate clinical assessment scales. While such scales are convenient tools in the clinical setting, it is often difficult to make use of all the information present in clinical assessment data when such data are analyzed using pharmacokinetic-pharmacodynamic (PK-PD) modeling. Therefore, it is of interest that better models for the analysis of such data are developed. 
Methods: This study relates modeling of recent data from a phase II study of a treatment against stroke. In the study, drug efficacy was monitored using the Scandinavian Stroke Scale (SSS). SSS is an ordered categorical scale, where several endpoints for neurological performance (speech, gait, motor performance, etc) are rated on several multi-item subscales. These ratings are subsequently added and summarized as a total SSS score. 
Results: We propose the use of a two-part modeling approach as a new tool for the modeling of data such as these. This approach is similar to that in a recently published study on alcohol use among teens [1]. Probabilistic models are used to describe the transitional properties of the data, thus explaining the probability of occurences of transition events such as dropout or a score decline, while linear models are used to relate the magnitude of the score change, given the observed transition. In this manner, the transition properties of the scale are taken into account, and the occurrence of random adverse events is modeled more realistically than if other available methods are used. 
Conclusion: We believe that our new approach may be useful not only for the analysis of SSS score data in the development of new treatments against stroke, but also in other therapeutic areas where aggregate clinical assessment scales are used in a similar manner. 
Reference: 
[1] M. K. Olsen and J. L. Schafer. A two-part random-effects model for semicontinuous longitudinal data. J. Am. Stat. Ass 96: 730-745 (2001) 

A PK-PD-disease model to support the design of clinical trials of drugs for the treatment of HIV

M. C. Rosario (1), P. Jacqmin (2), Pat Dorr(1), Manos Perro (1) & Elna van der Ryst (1)
(1) Pfizer Global Research and Development, Sandwich, Kent, UK; (2) Pharsight Corporation USA
oral presentation
Background: The viral dynamics of HIV infection have been widely studied and expressed as mathematical equations.  For most of the registered anti-HIV drugs, the pharmacokinetics are well characterized and some relationships with the viral load-time profiles in patients have been established. These models are nonlinear which implies that simple assumptions can produce complex dynamics.  The integration of these models in a PK-PD-disease model can help in better understanding the complexity of the interactions, and in the identification and clarification of the current assumptions. 
Methods: The present work describes the development of a generic PK-PD-disease model for a short-term (10-14 days) phase I/IIa study with an anti-HIV drug. The disease component is based on the model published by Bonhoeffer et al., which has been adapted for short-term treatment. It contains differential equations that describe the kinetics of the activated target cells, the actively infected cells, the latently infected cells and the virus. The parameters were derived from the literature, and from a model-based analysis of available phase I/IIa clinical data. The pharmacodynamic component that links the plasma concentrations of an anti-HIV drug to the inhibition of the virus growth is based on in-vitro measurements of drug potency. The links with the disease component take into account the mechanism of action of the drug (reverse transcriptase inhibition, protease inhibition, inhibition of entry), the difference in protein binding in-vitro and in-vivo and the uncertainties about the in-vitro in-vivo extrapolation. Finally, the pharmacokinetic component was based on information obtained from single and multiple dose escalation studies in volunteers as well as from clinical studies in patients. 
Results and Conclusions: Simulations have been performed to better understand the complexity of the interactions and to support the design of Phase I/IIa clinical trials of new anti-HIV drugs.  Finally, the model has aided the analysis and interpretation of the clinical data. 

Disease progression modelling; application of population analysis to distinguish between symptomatic and protective treatment effects.

Willem DeWinter(1), Joost DeJongh(1), Bart Ploeger(1), Richard Urquhart(2), Ian Moules(2), David Eckland(2), and Meindert Danhof(1)
(1)LAP&P Consultants, Leiden, The Netherlands. (2)Takeda Europe R&D, London, U.K.
oral presentation
Background: For certain diseases, drug treatment effects can only be evaluated relative to the disease progression over time. Model analysis of treatment effects requires that drug efficacy is expressed as an effect on the disease progression parameter(s). In earlier publications (1), the difference between symptomatic and protective effects of drug treatment has been discussed. For slowly progressing diseases, it is often difficult to discriminate between these types of effects, as the time-course of the clinical trial is limited relative to the duration of the disease. This problem becomes evident when the effect of a new drug is compared to that of existing treatments. In this case, not only the short-term efficacy is of interest. In particular, the difference in symptomatic and protective effects between the new drug and the existing reference therapies needs to be evaluated.
Methods: Results from two phase IV studies on treatment of type II (non-insulin dependent) diabetes melitus in over 2000 newly diagnosed patients were considered. Pioglitazone (Actos[R]), a new drug for treatment of type II diabetes, was compared to a reference treatment with either sulphonylurea or metformin for a treatment duration of up to one year. Disease progression was determined by taking blood samples for fasting plasma glucose (FPG) and glycated hemoglobin (HbA1c) over time. A population PD model was implemented in NONMEM in which the disease progression was modelled as a time dependent, saturable process that could be counter-acted by a protective or symptomatic treatment effect, or a mixture of both. FPG and HbA1c measurements were fitted to an indirect response model in which a cascade of events occurs in the following sequence: disease progression/treatment => FPG => HbA1c. 
Results: The model could be fitted to the data for patients in each of the three treatment groups for both FPG and HbA1c. The model cascade for these two biomarkers adequately described that the initial onset of the drug effect on FPG is followed by HbA1c, which has a somewhat slower onset. It was observed that for Pioglitazone treated patients, most of the drug effect could be classified as being protective; FPG and HbA1c levels decreased to a level that remained relatively stable during the course of treatment. For the sulphonylurea reference treatment, a substantial part of the drug effect was classified as symptomatic; After an initial period of decrease following the start of treatment, FPG and HbA1c levels started to rise slowly during the course of treatment. The metformin reference treatment, had characteristics of both protective and symptomatic drug effects. 
Discussion and conclusion: The present approach demonstrates that an appropriate disease progression model can be used to compare the effects on disease progression that are caused by different drugs. Besides the identification of quantitative differences between drugs, the model also offers the possibility to assess qualitative differences between drugs that become apparent during the course of treatment. The principle of the present analysis is not limited to diabetus melitus, but is applicable to a variety of chronic diseases with slow progression. In addition to retrospective analysis of trial results, this method has also been applied prospectively for the optimisation of trial designs in which identification of either protective or symptomatic drug effect is a primary objective. 
References: [1] Modelling of Disease and Disease Progression, N. Holford; in "Mechanism- Based PK/PD modelling as the basis for the development and validation of biomarkers". COST B15 Expert Meeting; April 27-28, 2000, Leiden, The Netherlands. 

Population Pharmacokinetic Modelling of a Subcutaneous Depot for GnRH Antagonist Degarelix

Christoffer W. Tornøe(1), Henrik Agersø(1), Henrik A. Nielsen(2), Henrik Madsen(2), and E. Niclas Jonsson(3)
(1)Clinical Pharmacology and Experimental Medicine, Ferring Pharmaceuticals; (2)Informatics and Mathematical Modelling, Technical University of Denmark; (3)Department of Pharmaceutical Biosciences, Uppsala University
oral presentation
Objectives: The objective of the present analysis is to develop a population pharmacokinetic model that describes the spontaneous subcutaneous (SC) depot formation of GnRH antagonist degarelix which is being developed for treatment of prostate cancer, exhibiting dose-volume and dose-concentration dependent absorption.
Methods: The pharmacokinetic analysis is made in NONMEM using data from two phase I clinical studies; an intravenous (IV) infusion study and a single SC dose escalation study. A two-compartment disposition model with first-order elimination from the central compartment is used to describe the pharmacokinetics of IV infusion of degarelix. The SC absorption is modelled using an approximation to Ficks' second law of diffusion out of a SC spherical depot. The fraction going into the outer spherical shell is estimated to account for the initial rapid SC release before the depot formation. The dose-volume effect on the SC release profile is modelled using a B-spline basis while the bioavailability is modelled as a function of the dose-concentration.
Results: The SC depot model is approximated by using two concentric spherical compartments where the volume of the outer spherical shell is estimated to approximately 15% of the depot volume. By means of the analytical solution to the partial differential equations of SC diffusion, the discretized compartment model yields sufficiently accurate results of the SC concentration. The estimation of the effective depot volume through the use of a monotone non-decreasing linear B-spline basis indicates that the volume effect is most apparent at low injection volumes while the effect fades out at higher injection volumes. The absolute bioavailability is estimated to decrease at increasing dose-concentrations.
Conclusion: The presented SC depot model describes the complicated pharmacokinetic profile of GnRH antagonist degarelix through joint analysis of IV and SC data. The SC release profile is successfully modelled using the principles of diffusion out of a spherical SC depot with the dose-volume and dose-concentration as controlling factors. This modelling approach might also be applicable for other depot formulated drugs exhibiting complicated pharmacokinetic profiles.

A Modeling Approach to Assessing Bioequivalence (BE) with Presence of Sparsely Sampled Subjects

C. Hu, J.Y. Kim, K.H.P. Moore, M.E. Sale
Clinical Pharmacology and Discovery Medicine, GlaxoSmithKline,
oral presentation
Objectives: Traditional BE assessment requires the evaluation of a 90% confidence interval (CI) for the ratio of AUC and Cmax for the test and reference formulation. AUC and Cmax must be obtained from every individual. However in many circumstances (e.g., pediatrics and adult patients), subjects may be sparsely sampled, making the individual evaluation infeasible. In such cases, population PK modeling seems appealing. The difficulty lies in the incompatibility between the exploratory nature of usual modeling process and the confirmatory nature of traditional BE assessment. Using conventional population PK modeling for BE would violate the principle of traditional BE assessment. E.g., if the formulation, as a covariate, was found "insignificant" in the model, BE would have to be declared by default. This is clearly unacceptable from the view point of traditional BE assessment. A paradigm presented here bridges the two approaches. 
Methods: The paradigm first develops a population PK model, with the aim of being consistent with the traditional BE assessment principle. From the final model parameters, the average AUC and Cmax can be predicted, and the ratio of average AUC and Cmax can be calculated. The BE assessment can then be made based on 90% CI for these ratios using bootstrapping. A detailed analysis plan following this paradigm was developed a priori for a BE-type assessment to examine GW433908 with and without ritonavir in healthy and HIV-infected subjects. 
Results: 1013 concentrations from 104 subjects in four studies were available. The fourth study was sparsely sampled, with 123 samples from 43 subjects. A population PK model was developed using NONMEM and the parameters were consistent with previously reported data. Then, 3000 bootstrap runs were conducted. The 90% CI for the AUC ratio was (0.908, 1.174). For Cmax, the CI for GW433908 alone was (0.951, 1.297). The CI for GW433908+ritonavir was (0.956, 1.244). The analysis between healthy and HIV-infected subjects demonstrated equivalence among AUC. For Cmax, equivalence was demonstrated for GW433908+RTV, and similarity was demonstrated for GW433908 given alone.
Conclusion: When sparse sampling is employed in patient studies, this paradigm provides a modeling approach resolving some of the controversies in BE-type assessments. 

Absorption and plasma kinetics of multiple high oral doses of glucose: influence of glibenclamide.

MR, Ballester, MJ Barbanoj, R Antonijoan, M Yritia, M Valle.
Centre d´Investigació de Medicaments, Servei de Farmacologia Clínica, HSCSP. Departament de Farmacologia i Terapèutica, UAB. Barcelona (Spain).
oral presentation
Objective: To develop a population model to describe the absorption and plasma time profile of glucose when multiple high oral doses of glucose are administered in healthy volunteers and the lowering effect of two different formulations of glibenclamide (a second generation sulphonylurea, commonly used for type-2 diabetes treatment). 
Methods: Twenty-four healthy volunteers of both sexes were enrolled in a placebo-controlled, randomized, single-blind, crossover study. After an overnight fast, 240ml of a 20% glucose solution was administered together with placebo, glibenclamide A (5mg) or glibenclamide B (5mg). Further, 60mL of 20% glucose solution was administered at 15min intervals up to 4h. Glucose plasma levels were assessed throughout Glucose analyzer (Hemoue(r)) before and at different times up to 16h postadministration. Population data analysis of glucose levels was performed employing NONMEM (version V) in three stages: (i) analysis of glucose absorption and plasma kinetics after its administration with placebo (ii) analysis of gibenclamide plasma kinetics (iii) modelling of glibenclamide effect. The effects of some of the collected covariates [age, gender, weight, creatinine clearance, smoking (either as continuous or categorical covariate)] were also examined. Results: Absorption of glucose was best modeled as a saturable process that follows Michaelis-Menten kinetics. Plasma levels of glucose were modeled employing a semi-physiological model: glucose levels were assumed to be due to the exogenous administration, and the endogenous synthesis and degradation in plasma. Taking into account the homeostatic processes that regulate glucose plasma levels, an extra compartment was added to the model representing the insuline. This compartment was assumed to have the same synthesis and degradation constant rate. Other assumptions of the model were (i) an increase in glucose levels induces an increase in the synthesis of insuline (linear model) (ii) insuline levels stimulates glucose degradation (linear model). After testing different models, the glibenclamide effect was incorporated as an inhibitory effect on the glucose degradation process. 
Conclusions: Saturation is observed in the absorption process when administering high oral doses of glucose. None of the administered glibenclamide formulations showed an onset of action rapid enough to avoid the first peak observed in the glucose levels. 

Assessment of the in vivo relative potency of the hydroxylated metabolite of darifenacin for the reduction of salivary flow using a population pharmacokinetic-pharmacodynamic meta-analysis

T. Kerbusch (1,2), U. Wählby (2), A. Skerjanec (3), P.A. Milligan (1), M.O. Karlsson(2)
(1)Pfizer Global Research & Development, Clinical Sciences, Department of Clinical Pharmacokinetics and Pharmacodynamics, Sandwich, Kent, UK, (2)Division of Pharmacokinetics & Drug Therapy, Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Uppsala, Sweden, (3)Novartis, Department of Clinical Pharmacology, Basel, Switzerland
oral presentation
Objectives: To estimate the in vivo potency of the hydroxylated metabolite (UK-148,993) to reduce salivary flow (SF) relative to that of the parent drug darifenacin (UK-88,525) in a wide range of studies using a population PK-PD approach (meta-analysis). 
Methods: PK and SF data from 337 and 262 individuals, respectively, were pooled from 17 Phase 1 studies and 1 Phase 2 study (median 28/33/30 and 7/7/8 darifenacin/metabolite/SF observations per healthy volunteer and patient, respectively). Data encompassed 1 i.v., 5 different p.o. formulations (1-45 mg total daily dose) and CYP3A4 inhibitors resulting in a wide range of parent-metabolite concentration ratios. 
Results: NONMEM (V & VI) was used to describe the population PK of darifenacin and its hydroxylated metabolite with a two-compartment disposition models with first order absorption. The PK model for darifenacin included covariates characterising the influence of formulation (70-110% higher bioavailability (F) for extended release compared with immediate release), dose (dose-nonlinearity 1.1 to 1.35-fold over the dose range studied) and CYP2D6 genotype (heterozygote-EM and PM 40 and 90% higher exposure than a homozygote-EM, respectively). The presence of ketoconazole or erythromycin increased darifenacin F to approximately 100% and ketoconazole additionally decreased clearance (CL) by 68%. CL was 31% lower in females and 10% lower at night. F was 56% lower in Japanese males. Ketoconazole and erythromycin also decreased metabolite exposure by 61.2 and 28.8%, respectively. Interindividual variability in the residual error model of darifenacin was described using a generalized least squares approach. 
A binding-model yielded a better description of the decrease in SF compared to a direct-effect, indirect-effect or link model, by fully accounting for the time-course of the PD effect. Internal validation demonstrated robustness. Covariate analysis identified a circadian rhythm in SF. The model, with confidence intervals (CI) determined by likelihood profiling, indicated the relative potency of the metabolite to darifenacin to reduce SF at 11.1% (95% CI: 3.8%, 19.6%). This implied that the metabolite was 9-fold less potent than darifenacin in vivo. The in vivo protein binding-corrected relative potency was estimated at 2.1% (metabolite 50-fold less potent). The model indicated that no other metabolites contributing to the SF were likely to be formed during first-pass and that no sensitisation or tolerance development was evident over time. The subjective measurement of dry mouth (DM) is not directly linked with the objective measurement of drug-induced SF.
Conclusions: The meta-analysis provided a descriptive integration of main characteristics and covariates of the PK of darifenacin and its metabolite, enabling interpolation and extrapolation of these key-factors. Population PK-PD modelling was used to assess the in vivo potency of the metabolite for the decrease in SF relative to that of the parent drug. Metabolite contribution to this effect was negligible. 
References:
[1] Thomas Kerbusch, Ulrika Wählby, Peter A. Milligan, Mats O. Karlsson. Population pharmacokinetic modelling of saturable first pass metabolism, CYP2D6-genotype and formulation-dependent bioavailability of darifenacin and its hydroxylated metabolite in a meta-analysis (submitted). 
[2] Thomas Kerbusch, Peter A. Milligan, Mats O. Karlsson. Assessment of the in vivo relative potency of the hydroxylated metabolite of darifenacin for the reduction of salivary flow using a population pharmacokinetic-pharmacodynamic meta-analysis (submitted). 

Dose-Timing Information Improves The Clinical Explanatory Power Of Data On Patient Adherence To Antiretroviral Drug Regimens

B. Vrijens(1-2), S.L. Mayer(1),R.Rode(3), R. Bertz(3), J. Urquhart(1)
(1) AARDEX Ltd., Zug, Switzerland; (2) Dept of Biostatistics, University of Liège, Belgium; (3) Abbott Laboratories, Chicago, United States
oral presentation
Objectives: Variable adherence to prescribed antiretroviral (ARV) therapy in HIV-infected individuals may result in variable exposure to the ARV drugs used. Large deficits in ARV drug exposure clearly have a negative effect on virologic outcomes, [1-3]; however, appreciable rates of virologic failure are seen even in patients who take >95% of prescribed doses, suggesting that dose-timing errors play a crucial role in virologic failure. This analysis aims to assess the effect of variations in ARV dose-timing on virologic response measured repeatedly over time in HIV-infected individuals.
Methods: The analysis from this phase I/II randomized clinical trial involved 35 ARV-naïve, HIV-infected individuals, prescribed lopinavir/ritonavir (QD: 800/200 mg or BID: 400/100 mg), stavudine, and lamivudine. Observations on plasma viral load (VL; copies/mL) were categorized into 4 clinically meaningful states, 0-49, 50-399, 400-1999, and >1999. A time-dependent continuation ratio model was used to analyze longitudinal ordinal responses. Several measures of adherence were investigated including taking compliance, correct dosing, and time spent below EC50. A new variable, Timing Error, was derived from the third moment of the inter-dose interval distribution. Explanatory power for changes in VL of each adherence parameter was assessed through changes in model deviances.
Results: Improvement and deterioration in VL were modelled separately and both were significantly associated with lopinavir plasma concentration (p=0.0002 and p<0.0001, respectively). The most significant PK-derived predictor, the time that Internal Exposure fell below the EC50, appeared to be insensitive to between-patient variability in PK parameters. Changes in VL were most significantly driven by within-patient dose-timing errors. For example, the probability of VL deteriorating from 0-49 to >50 copies/mL was 8% for perfect dose-timing and 14% for "moderate" Timing Errors. 
Conclusion: Dose-timing information increases the explanatory power of patient adherence data and its association with ARV treatment outcomes. After initial viral suppression, lopinavir/ritonavir was not highly dependent on Timing Errors. Further research is needed to evaluate the relative "forgiveness" of lopinavir/ritonavir and other drugs regarding Timing Errors. This analysis reveals a potential reason for virologic failure and can also guide the practitioner in determining when to consider an adherence intervention strategy. 
References
[1] Paterson DL, Swindells S, Mohr J, et al. Adherence to protease inhibitor therapy and outcomes in patients with HIV infection. Ann Int Med 133: 21-30, 2000. 
[2] Liu H, Golin CE, Miller LG, et al. A comparison study of multiple measures of adherence to HIV protease inhibitors. Ann Inter Med 134: 968-77, 2001.
[3] Arnsten J, Demas P, et al. Antiretroviral therapy adherence and viral suppression in HIV-infected drug users: comparison of self-report and electronic monitoring. Clin Inf Dis 33: 1417-23, 2001.

Population pharmacokinetics/-dynamics of dabigatran, the active form of the new oral direct thrombin inhibitor dabigatran etexilate (BIBR 1048) in patients undergoing hip replacement

Joachim Stangier, Karl-Heinz Liesenfeld, Christiane Tillmann, Inaki Troconiz (#), Hans Guenter Schaefer
Boehringer Ingelheim Pharma GmbH & Co. KG, (#) School of Pharmacy, University of Navarra, Pamplona, Spain
oral presentation
Introduction: The oral direct thrombin inhibitor prodrug dabigatran etexilate is under development for the prevention of thrombosis in patients at risk of thrombotic events. The population pharmacokinetics and pharmacodynamics of dabigatran were assessed in a dose escalation safety study (BISTRO I) involving 289 patients treated with 12.5 to 300 mg dabigatran etexilate. This trial was the first study with dabigatran etexilate in patients. The aim of the population PK/PD analysis was to provide information on pharmacokinetics and dynamics in orthopaedic patients in order to support dose selection and rational planning of further clinical studies with the new oral thrombin inhibitor for prevention of deep vein thrombosis. 
Methods: Dabigatran plasma concentrations and the pharmacodynamic parameters activated partial thromboplastin time (aPTT) and ecarin clotting time (ECT) were measured. In total, about 5000 PK and PD data from 287 patients were included in the pharmacokinetic/-dynamic population analysis. Pharmacokinetic and pharmacodynamic models were developed independently. Population PK and PD models were developed using NONMEM (Version 5). The influence of patient characteristics on the pharmacokinetic and -dynamic model parameters were investigated. 
Results: Pharmacokinetics of dabigatran were best described by a two- compartmental body model with first order absorption and elimination. The pharmacokinetics of dabigatran are different during the initial 24 hours after surgery. The rate constant of drug absorption KA was significantly lower than KA on days 2-10 of treatment. This is most likely due to alterations in gastric motility after surgery. Dabigatran clearance was significantly correlated with the calculated serum creatinine clearance. This was to be expected because renal excretion of unchanged drug is the principal route of elimination. The higher age and the lower renal function of the patient population accounted for the fact that they had lower plasma clearance than young healthy volunteers. Dabigatran plasma concentrations and the blood coagulation parameters aPTT and ECT displayed a close correlation. The relationship of dabigatran concentration and aPTT was best described by a combination of an Emax and a linear model. ECT was linearily related to dabigatran concentrations in plasma. The magnitude of the PD response was apparently higher early after surgery and decreased with time. This time dependent variations in aPTT and ECT response might be rationalised by surgical effects on haemostasis caused by transfusion of large fluid volumes during operation. 
Conclusions: Population pharmacokinetic analysis showed that differences exist in the pharmacokinetics of dabigatran between the initial 24 hours after surgery and days 2 - 10 of treatment. Effects of surgery on drug absorption required further investigations of the absorption of direct thrombin inhibitors administered orally early after orthopaedic surgery. The population pharmacodynamic investigation of the direct thrombin inhibitor dabigatran revealed a close correlation between drug plasma concentrations and prolongation of blood coagulation. The prolongation of aPTT and ECT by dabigatran was apparently more pronounced early after surgery. The population PK and PD models were employed to simulate the dose response relationship of dabigatran in order to support dose selection and planning of further clinical trials with the dabigatran in prevention of deep vein thrombosis after orthopaedic surgery. 

Applications of Distributed computing in Drug development

Mark Sale
Clinical Pharmacology and Discovery Medicine, GlaxoSmithKline, 5 Moore Drive, RTP NC
oral presentation
Objective: Improve speed and robustness of NONMEM analysis.
Methods: Distributed computing is a collection of methods that permit the application of many computers to solve a computationally intensive problem. The key to the ability to use distributed computing is the ability to break the problem into appropriately sized pieces. In biological sciences the most common use for distributed computing is in computational chemistry. Two applications in this area are BLAST [1] and GOLD [2]. Two applications in modeling and simulation have found distributed computing to be useful. Entelos's Physiolab uses 145 computers to perform Monte Carlo Simulations for complex physiological models [3]. In addition to applications in computational chemistry, GSK has applied distributed computing to automated model selection with NONMEM, using a Genetic algorithm based approach.
Genetic Algorithm is a discrete space search algorithm based on the mathematics of evolution/survival of the fittest. Preliminary work suggests that this approach is more robust than the conventional forward addition method of model selection [4]. The limitation of this approach is that it is inefficient, requiring the evaluation of thousands of models to insure robustness in finding the optimal solution. However, Genetic algorithm is very well suited to distributed computing, as a "population" of several hundred NONMEM models is created at a time, each being independent of the others. Each model in a "generation" then can be sent to a separate computer for minimization and the results returned. The application of distributed computing to Genetic algorithm model selection in NONMEM has made the approach practical, with typical analyses, comprised of several thousand model runs requiring only a few days.
Results: Distributed computing increases the speed of Genetic Algorithm model selection in NONMEM by up to two orders of magnitude. This permits the assessment of a sufficient number of models (typically 5000) to insure robustness of the analysis.
Conclusions: Genetic Algorithm with distributed computing is a promising technology to provide dramatic improvements in speed and robustness of NONMEM analysis.
References: 
[1] Madden T, Tatusov R, Zhang J. Applications of network BLAST server Meth. Enzymol. 266:131-141. 1996
[2] Jones G, Willett P, Glen RC. Molecular recognition of receptor sites using a genetic algorithm with a description of desolvation. Journal of Molecular Biology. 245(1):43-53, 1995
[3] Metz, C. Grid computing: Case Study - Entelos. PC Magazine Jan 2003.
[4] Bies R, Sale M, Smith, G, Muldoon, M. Lotrich F, Pollock, B. Outcome of NONMEM analysis depends on modeling strategy, Clin Pharm Ther, 73(2) 2003 (abstract)

Parallel computing under Linux

Lars Lindbom
Div. of Pharmacokinetics and Drug Therapy, Dept of Pharmaceutical Biosciences, Uppsala University, Sweden
oral presentation
Objectives: According to Moore's law [1], there is an exponential growth in the number of transistors per integrated circuit over time, doubling the computational power of our laptops, desktops and servers every 18 months. Consequently, the time it takes to perform a fit of a specific pharmacokinetic/pharmacodynamic model is shortened every year. Today, model fits of simple PK models typically takes a few seconds to execute, moderately complex PK/PD models maybe around ten minutes while the most complicated models still require 24 hours or more to finish. Single runs are hence manageable. There are however situations when multiple runs are needed, e.g. to carry out stepwise covariate model building, to obtain standard errors of parameter estimates through a bootstrap or to perform randomization tests to achieve true significance levels of adding covariate effects to a model. These methods, involving hundreds or thousands of runs, are extremely CPU time consuming and today intractable for all but the simplest models. This will, if Moore's law continues to be valid, eventually change in a not too distant future. However, if we want to be able to use these methods today or to explore future methods, we need to exploit our existing computing power more efficiently.
Methods: One way of avoiding the problem is to identify the parts of a computer intensive task that can be solved independently from each other. The task should be restructured in such a way that the independent tasks can be run in parallel. Parallelized problems can easily be run on multi-processor computers using standard operating system calls. To take the parallelized approach further, we may also use multiple computers in a cluster. The development of cluster solutions for inexpensive computers has been very rapid over the last years, boosted by the concurrent development of the open source operating system Linux.
Results: A cluster has been set up, consisting of five dedicated dual-cpu servers plus five user desktops yielding in total 15 processors, connected by fast Ethernet network. The computers are all running Red Hat Linux 7.3 with kernel 2.4.19 including the single system image (SSI) cluster patch openMOSIX [2]. On top of this an application programming interface to NONMEM, Perl-speaks-NONMEM or PsN, has been developed that enables parallel execution of NONMEM runs within Perl scripts. The theoretical gain in speed for an application running multiple NONMEM jobs on this cluster is approximately 15 times thereby enabling the use of computer intensive methods for at least moderately complex models. This solution is very easy to expand by adding new computers, thereby allowing the cluster to grow as the need for computing power increases.
Conclusions: Without any modifications, a cluster using Linux and openMOSIX is very good for load-balancing of multiple computer intensive applications, especially if the run times exceed ten seconds. Methods running multiple NONMEM jobs will benefit dramatically from the distributed computing power of this type of cluster. The modeling process can potentially change if computer intensive methods are available not only for the simplest problems.
References
[1] G. E. Moore, Cramming more components onto integrated circuits, Electronics 38 (1965) 114-117.
[2] openMOSIX Homepage, http://openmosix.sourceforge.net, (1/4 2003)

Patient adherence and the evolution of resistance to anti-viral agents

Roy Anderson
Department of Infectious Disease Epidemiology, Faculty of Medicine, Imperial College, London, UK
oral presentation
The paper will discuss recent work on the interplay between patient adherence and the evolution of drug resistance in HIV-1 to anti-retrovirals. Mathematical models are described that meld pharmacokinetics, pharmacodynamics, within-host viral population growth and patient adherence. These models are parameterised by reference to defined anti-retrovirals, pathogenesis studies of HIV-1 in cohorts with known dates of seroconversion and data from the use of medication event electronic monitoring (using MEMS caps). Conclusions are drawn about the effects of drug holidays, and periods of poor adherence, on the likelihood of treatment failure.

A Mechanism-Based PK/PD Model Predicts the Time-Course of Hematological responses for Epoetin beta

N. Hayashi(1), K. P. Zuideveld(1), P. Jordan(2), R. Gieschke(1)
(1) Modeling & Simulation Group; (2) Biometrics, F. Hoffmann-La Roche AG, Basel, Switzerland
oral presentation
Objectives: The objective was to develop a Mechanism-Based PK/PD model that predicts the time courses of hematological responses after administration of Epoetin beta using data from a study in healthy volunteers. Furthermore, simulations were used to assess whether the model is able to predict published efficacy data in renal anemia patients.
Methods: The population PK/PD analysis was performed using NONMEM based on serum concentrations of Epoetin beta, reticulocyte, Red Blood Cell (RBC), Hemoglobin (Hb), and Hematocrit (Ht). 
The mechanism-based model was developed on the basis of data from a clinical pharmacology study in 43 healthy volunteers. The time profiles of hematological variables in patients were simulated and compared with the published study's results in renal anemia patients. 
Results: The model includes the concepts of "an Emax model for the effect of the drug on RBC production rate", "a homeostatic negative feed back by Hb on the RBC production rate", "an identical life span for all RBC", and "the amplified changes in reticulocyte count caused by the immature reticulocyte increase". Population mean values for Emax and EC50 were 4.74 x104/mL/day and 25.2 mIU/mL, respectively. For the simulations of hematological responses in patients, the baseline values of RBC observed in patients were used. As a result, satisfactory predictions for patients were obtained for not only the mean values but also the inter-individual variability in all hematopoietic responses. The observed hematological responses for the patients with renal anemia were within the 80% confidence interval predicted by the model.
Conclusion: A mechanism-based PK/PD model was developed and is able to describe the time courses of hematological responses for Epoetin beta in healthy volunteers and in patients. 

Comparison of the pharmacokinetics of S-1, an oral anticancer agent, in Western and Japanese patients

Emmanuelle Comets(1, 3), Kazumasa Ikeda(2), Yusuke Tanigawara(3)
(1) Inserm E0357, Hopital Bichat-Claude Bernard, Paris, France (2) Taiho Pharmaceutical Co, Ltd., Tokushima Research Center, Tokushima, Japan (3) Department of Pharmacy, Keio University Hospital, Tokyo, Japan
oral presentation
Objective: S-1 is an oral anticancer agent combining tegafur (FT), a prodrug of 5-fluorouracil (5-FU), with potassium oxonate (oteracil) and gimeracil (CDHP) respectively to mitigate gastrointestinal toxicity and increase the half-life of 5-FU. This article presents a population pharmacokinetic analysis of these four compounds in Western cancer patients. The second objective was to compare the pharmacokinetics of S-1 in Western patients to the pharmacokinetics in Japanese patients described in a previous analysis. 
Methods: A single dose (25-45mg/m2) of S-1 was administered to 60 patients. In each patient, 6 concentrations of FT, 5-FU, oteracil and CDHP were measured over 24hr. Using NONMEM, oteracil and CDHP were analysed separately, and the individual estimates of CDHP parameters were included in the joint analysis of FT and 5-FU. We used validation techniques to assess differences between the two populations. Finally we compared the exposures in Western and Japanese patients using simulations, based on the results of the analyses performed in each population separately. 
Results: A compartmental model describing the PK of the 4 compounds was developed. The influence of CDHP on the elimination of 5-FU was well described by an enzymatic inhibition model. The model provided a good fit for all compounds. The pharmacokinetics for oteracil were similar between Western and Japanese patients. Although the pharmacokinetics for FT were different between the two populations, apparent differences in exposure to its metabolite 5-FU resulted mostly from different total doses, due to different body sizes. 

Pregabalin Exposure-Adverse Event Analysis in Patients With Neuropathic Pain, Generalized Anxiety Disorder, or Partial Seizures

Miller R, Kowalski KG, Liu J, Frame B, Burger PJ, Corrigan BW, Bockbrader HN, Lalonde R.
Pfizer Global Research and Development, Ann Arbor, MI 48108, USA.
oral presentation
Objective: To describe the pregabalin exposure-adverse event (dizziness and somnolence) relationship following pregabalin doses in patients with neuropathic pain, generalized anxiety disorder, or partial seizures.
Methods: Patient daily adverse event (AE) scores for the 2 most prevalent AE's (dizziness and somnolence), were combined from 8 neuropathic pain studies, 3 studies in patients with partial seizures, and 6 studies in patients with generalized anxiety disorder. All studies were randomized, double-blind, multiple dose (TID or BID regimens), placebo-controlled, parallel-group multicenter studies. A mixed-effects proportional odds model was used to characterize the relationship between the probability of an adverse AE score (dizziness and somnolence) using a 4 point ordered categorical scale (none, mild, moderate, severe) and pregabalin exposure in individual patients. Two classes of drug models were considered for both dizziness and somnolence AE's, Emax-type and linear dose-response.
Results: The dataset consisted of 194,087 observations collected in 4459 subjects. Of these, 63,059 observations were from the placebo group; 6698 were from the 50 mg/day group; 5200 were from the 75 mg/day group; 31,335 were from the 150 mg/day group; 2773 were from the 200 mg/day group; 22,652 were from the 300 mg/day group; 6829 were from the 400 mg/day group; 5386 were from the 450 mg/day group; and 50,155 were from the 600 mg/day group. The percent of adverse event observed over the duration of the trial by pregabalin daily dose is presented in Table 1. 
Table 1. % Adverse events observed by pregabalin daily dose.	
	Dizziness	Somnolence	
Daily Dose mg/day	None	Mild	Moderate	Severe	None	Mild	Moderate	Severe	
Placebo	97.1	1.9	0.88	0.09	95.7	3.2	0.97	0.07	
50	96.6	2.5	0.93	0.00	96.5	0.85	2.66	0.00	
75	98.3	1.5	0.13	0.00	97.7	1.88	0.10	0.37	
150	94.3	3.9	1.37	0.36	93.1	4.48	2.34	0.10	
200	88.3	8.5	3.03	0.14	83.6	13.2	2.74	0.54	
300	87.5	9.2	3.13	0.18	88.7	7.4	3.39	0.48	
400	84.0	10.4	5.04	0.63	86.6	9.53	3.90	0.00	
450	85.6	9.5	4.27	0.61	83.3	9.47	6.47	0.82	
The sigmoid Emax model was considered the best base model to further explore fixed effect relationships. The initial models that describe the severity of dizziness and somnolence using a 4-point ordered categorical response resulted in an extremely bimodal distribution of the empirical Bayes predictions of the ETAs, the ETABAR. A histogram plot demonstrated a primary mode near zero (patients who have no AE's) and a secondary mode of extremely large values (patients with an AE). The mean ETA's were significantly different from zero for dizziness (ETABAR = 2.2 [p <0.5 x 10-229]) and somnolence (ETABAR = 2.3 [p <0.16 x 10-189]). These histograms clearly showed that the distribution of ETA's violated the normality assumption. An attempt to solve this problem was made by applying a 2-stage approach in which separate models were developed for the incidence of AE and for the severity of AE given that an adverse event has occurred. The probability for incidence of dizziness and the conditional probability for severity of dizziness were then used to obtain joint and marginal (unconditional) probabilities for severity of dizziness. 
For the incidence model, a sigmoid Emax model adequately describes the dose-response for incidence of dizziness and somnolence. In both cases, the appearance is relatively abrupt with low occurrence of dizziness or somnolence at daily doses less than 150 mg/day. The conditional severity for dizziness and somnolence were well-described by a sigmoid Emax model that took into account a time-dependent exposure effect as well as a time-dependent attenuation of dizziness and somnolence. The rate constant (ke0) of appearance of dizziness with respect to initiation of pregabalin dosing was 1.18 days-1 which corresponds to a half life of appearance of 0.63 days. The rate constant (ke0) of appearance of somnolence with respect to initiation of pregabalin dosing was 0.595 days-1 which corresponds to a half-life of appearance of 1.2 days. These values for onset of AE are consistent with the pregabalin half-life of 6.3 hours and the accumulation of pregabalin plasma concentrations to steady state. The rate constant for attenuation of dizziness was 0.0889 days-1 which corresponds to a half-life of 7.8 days. The rate constant for attenuation of somnolence was 0.101 days-1 which corresponds to a half-life of 6.9 days. These values reflect a decrease in dizziness and somnolence that would reach a new steady state in about 3 to 4 weeks. The results suggest that the probabilities of experiencing dizziness and somnolence during pregabalin treatment increase with pregabalin daily dose. The predicted mean incidence of dizziness or somnolence was at least 2-fold higher at doses 200 mg/day compared to daily doses ≤150 mg/day. Overall, the risk of moderate or severe dizziness or somnolence at any time following pregabalin administration was low (<7% on average). The model predicted risk of moderate or severe dizziness or somnolence increased from <5% on Day 1, peaked at <10% on Day 6, and declined to values of <6% by the end of 4 weeks. To assess the impact of dropouts on this apparent attenuation of AE's a data set was created in which the last observation carried forward (LOCF) was included for dropouts. The frequency based estimates of the unconditional cumulative probabilities were obtained by averaging the number of observed AE scores ≥m at each time. The time trend observed in the frequency-based probabilities was not as pronounced as the observations for patients without LOCF, however, the tendency in the attenuation was still apparent.
Conclusions: The probability of AE's increases with dose and is most evident at daily doses of 200 mg/day and greater. The risk of an AE at any time following administration of pregabalin increases to reach a maximum on Day 6 and declines to reach a plateau by the end of 4 weeks.

Population Pharmacokinetics of Intravenous Busulfan in Children

Brunhild Schiltmeyer1, Joachim Boos1, Matthias Schwab2, Thomas Mürdter2, Thomas Klingebiel3, G. Fleischhack5, Josef Vormoor1, Bernd Gruhn4 and Georg Hempel1
1 Universitätsklinikum Münster, Klinik und Poliklinik für Kinderheilkunde, Pädiatrische Hämatologie/Onkologie, Münster; 2 Dr. Margarete Fischer-Bosch-Institut für Klinische Pharmakologie, Stuttgart; 3 Klinik für Kinderheilkunde III - Pädiatrische Hämatologie und Onkologie, Klinikum der Johann-Wolfgang-Goethe-Universität, Frankfurt; 4 Klinik für Kinderheilkunde III - Pädiatrische Hämatologie und Onkologie, Universitätsklinik Jena; 5 Universität Bonn, Zentrum für Kinderheilkunde, Pädiatrische Hämatologie/Onkologie, Bonn, Germany
oral presentation
Background: High-dose busulfan (bu) is an important part of many conditioning regimens before autologous or allogeneic bone marrow transplantation in children. Problems arise with oral bu due to high intra- and interpatient variability in the apparent clearance resulting in a varying systemic exposure, measured as the area under the curve (AUC). A new intravenous (i.v.). formulation (Busulfex(tm)) was developed in 1999 in order to reduce both intra- and interindividual variability of bu pharmacokinetics (PK). 
Objective: To evaluate the PK of the new i.v. formulation of bu in children with the purpose to produce a dose intensity similar to that achieved by oral bu with a lower interindividual variability of the AUC (target AUC 1600 ± 600 µM x Min). 
Methods: Overall, 19 children from 4 clinical sites were included into the trial (Median: 4 years, range: 0.9-16.1). They received 80% of the required oral bu dose according to the respective protocol in 15 doses with the first infusion over 4 h and the following administrations given 12 h thereafter over 2 h every 6 h. PK sampling was performed with 7 samples from the first dose, 2 trough levels from intermediate doses and 5 optional samples from the last dose. The samples were analysed for bu using a new LC-MS-method requiring only 200 µl of plasma. Pharmacokinetic modelling was performed by using NONMEM.
Results: Bu kinetics were best described by a one-compartment model. The best fit was obtained with calculations based on the actual body weight as a covariate for Clearance (Cl) and Volume of distribution (V). The final parameter estimates were: Cl 0.18 l/h kg ± 20% and V 0.38 l/kg ± 49% (population mean ± interindividual variability). Inclusion of a parameter for IOV (interoccasion variability) on Cl (11%) improved the fit. The AUC after the 1st dose (AUC 1st dose / 2) ranged from 850-1670 µMol x Min (geometric mean = 1200 µMol x Min, CV = 16%, n=18). In 2 out of 18 patients, the AUC after the 1st dose was out of the target range. The AUC after the last dose ranged from 1090-1790 µMol x Min (Geom. mean = 1310 µMol x Min, CV = 16%, n=10). After the last dose, the AUC of all patients was in the target range. 
Conclusion: Our results suggest that i.v. bu can reduce the interpatient variability in systemic exposure compared to oral bu (CV of 16% after i.v. bu vs. CV of 37% after oral bu). The applied dosing of i.v. bu with 80% of the oral standard dose appears to be too low. Comparison with oral data is ongoing. 

Maximum likelihood estimation in nonlinear mixed effects models

Estelle Kuhn and Marc Lavielle
University Paris-Sud, France
oral presentation
Objectives : Our aim is to estimate parameters in non linear mixed effects models by maximum likelihood. Some well-knomw used methods are based on linearization of the likelihood. The properties of these estimator depend inter alia on the number N of observed subjects and on the number n_i of observations for the ith subject. For example, FO ensures no convergence of its estimator and FOCE converges only under the assumptions that n_i is equal to infinity for all subjects. We propose a method based on a stochastic approximation version of the EM algorithm, denoted SAEM, for which these restrictive condition mustn't be checked : the produced estimator converge toward a local maximum of the likelihood under very general regularity conditions on the model. SAEM also yields an estimation of the likelihood of the observations and a confidence interval for the estimated parameters. 
Method : The expectation-maximization (EM) algorithm is a broadly applicable approach for the iterative computation of maximum likelihood estimates, useful in a variety of incomplete-data (or partially-observed-data) statistical problems. In a mixed effects model, the random effects can be considered as the non observed data. Then, EM can be used for estimating the parameters of a linear model, but the E-step becomes untractable whenever the model is non linear. SAEM replaces the E-step by a simulation step: at each iteration, the random effects are drawn with the conditional distribution and the parameters are updated using these simulated data. Furthermore, the simulated random effects allow to estimate the likelihood of the observations as well as the Fisher information matrix. 
Results : This algorithm converges very quickly to the maximum likelihood estimator. We implemented SAEM on the pharmacodynamic simulated example used by Walker on 50 replications [1] : the relative root means square errors (RMSER) are lower than those obtained by FOCE, Laplacian methods and also the Monte Carlo EM proposed by Walker. We also compared the results of SAEM with FOCE on a pharmacokinetic simulated example used by Concordet [2] on 20 replications: the RMSER of the SAEM algorithm are also lower than with FOCE, particularly for the variability. 

Design and power PK/PD experiments using very sparse data

Gianluca Nucci and Roberto Gomeni
Clinical Pharmacokinetics/Modelling and Simulation, GlaxoSmithKline, Verona, Italy
oral presentation
Objectives: The design of PK/PD experiments is a critical issue for improving the efficiency of pharmacology trials. An optimal design should account for the number and timing of samples, inter-individual variability, prior information on mechanistic model structure and parameter values, and, finally on the practical constraints linked to the feasibility of the experiment. In drug development the number of PK/PD samples that can be obtained may be limited to only one PK and PD measurement for practical (destructive sampling) or ethical reasons (exposure to radiation in imaging experiments). In this work we propose a novel method to design and power very sparse PK/PD experiments (one PK/PD sample per subject) accounting for inter-/intra-individual variability on PK and PD measurements and uncertainty on structural model parameters 
Methods: Initially, the proposed approach optimized the Fisher population information matrix (1) using a grid search algorithm, for the selection of optimal sparse sampling times (one sample/subject). The PD fixed and random effect model parameters were assumed precisely known from previous experiments and the PD was assumed driven by error free PK. Then, we relaxed these hypotheses assuming uncertainty on PD prior parameter estimates and inter-/intra-subject variability on PK measurements. Finally, the power of the optimally designed experiment was estimated by adjusting the sample size based on the expected parameter precision while the validation of the optimal design was assessed by evaluating bias on simulated experiment outcomes. 
Optimal design and Simulation Results: A one-compartment model characterized the simulated PK profile with a PK/PD link described by an Emax model with uncertainty on EC50 expected in the 8-16 ng/ml range and on Emax expected to lie between 80 and 100 %. Inter-individual variability for each model parameter was assumed log normal with a CV of 10% and measurement error assumed to be additive (variance=25). The optimal design was based on one sample/subject and four PD measurements that were: 2 hours post dose (PK Tmax) and 15, 18 (times related to the range of EC50 values explored) and 24 hours post dose (the latter being the time point corresponding to PK Cmin). The simulation study indicated that this design provided unbiased estimates for any parameter randomly selected within the uncertainty domain. The precision of parameter estimates was heavily linked to the number of subjects tested and to a lesser extent to the PK variability levels. Changing the expected PD variability had a noticeable impact on both bias and precision of estimates. 
Conclusion: The methodology developed addresses for the first time the impact of uncertainty in the parameters driving the design optimization for very sparse PK/PD experiments. The proposed approach showed that one measurement per subject and four subjects were sufficient to obtain unbiased PK/PD parameter estimates while an acceptable precision on the model parameters (<20%) required at least 16 subjects using a sparse sampling design.
Reference Retout S, Duffull S, Mentre F. Comput Methods Programs Biomed 65, 141-51, 2001 

Estimating population pharmacokinetic parameters when dose and dose-time are not known accurately

Duffull SB (1), Isbister GK (2), Dawson AH (2), Hackett LP (3), Whyte IM (2).
(1) School of Pharmacy, University of Queensland, Australia. (2) Discipline of Clinical Pharmacology, University of Newcastle, Australia. (3) Clinical Pharmacology and Toxicology, Western Australian Centre for Pathology and Medical Research, Australia.
oral presentation
Introduction: Understanding the PKPD relationship of therapeutic agents when used in overdose is paramount for the development of treatment guidelines. In deliberate self-poisonings involving therapeutic agents it is often difficult to gain accurate information on the dose taken and the exact timing of the dose. The attending clinician may be able to ascertain some of this information from the patient or relatives at the time of admission and grade the veracity of this information. 
Aim: To develop a population pharmacokinetic model for citalopram when taken as a deliberate overdose and when dose and dose-time may not be known accurately.
Methods: Eighty nine plasma citalopram concentrations were available from 29 patients. The data were modelled by means of a Monte Carlo Markov chain method using WinBUGS (ver. 1.3). Model building was based on assessment of the posterior distribution of the log-likelihood. A one-compartment model with first-order input and first-order elimination provided a good description of the data. The prior distribution for CL and V were set to be minimally informative as multivariate normal with mean values of 30 L/h and 900 L (typical values from therapeutic use studies), respectively. The prior for Ka was set to 0.5 hours (with high precision [i.e. low variance]) based on literature reports for therapeutic use, since there were few samples before 4 to 6 hours post-dose. Between subject variability was assumed to be log normal with low information priors for all parameter values. In addition, the fractional dose taken and lag-time were also estimated. Both were assumed to be normally distributed with a mean of 1 and 0, respectively. The precision was indexed to the veracity of the knowledge of dose and dose-time. Veracity was reported on a 4 point ordinal scale.
Results: The posterior mean of CL was 29 L/h (between-subject variability = 41%), and for V was 760 L (between-subject variability = 51%). The estimated actual dose ingested ranged from 0.29 to 1.40 times the nominal dose recorded. The estimated actual time of dose ingestion varied from 1.6 hours before to a few minutes after the nominal dose-time. Inclusion of informative priors on dose and dose-time improved overall model fit and decreased between subject variability in CL by 43% and in V by 1%.
Conclusion: The use of informative priors where the informativeness was indexed to clinical findings, within the framework of a fully Bayesian analysis seemed to improve the predictive ability of a model developed from pharmacokinetic data arising from self-poisonings with citalopram.

Potential consequences of drug non-compliance on the therapeutic / iatrogenic effects of oral anticoagulant therapy : an in silico study.

A.Blesius (1), S. Chabaud (1), M. Cucherat (1), P. Mismetti (2), JP. Boissel (1), P.Nony (1).
(1)Clinical Pharmacology Department, EA 643, Cardiovascular Hospital, Lyon, France; (2)University Hospital Bellevue, Saint-Etienne, France.
poster
Objectives: In relation to their narrow therapeutic index, oral anticoagulant agents are often under prescribed, too low doses leading to thromboembolic events, and over-dosing being responsible for haemorrhagic complications. In the USA the proportion of treated patients with serious bleeding events is estimated at between 3 and 7.5% per year, and the annual percentage of related deaths is estimated to be 0.2%. On the other hand, the annual incidence of thromboembolic complications related to inadequate decoagulation is estimated at 5%. In order to better define the choice of oral anticoagulant agent and its dosage regimen in case of poor compliance, we performed an “in silico” study. 
Methods: Six months therapy was simulated at steady-state in 30 patients for warfarin (W) and acenocoumarol (A), using five different profiles of poor compliance. The numerical simulation used widely described determinist PK-PD models of the two drugs [1,2,3] and generated consecutive dosing intervals in a stochastic way (truncated Gauss distribution, Markov regression process). Since drug non-compliance has many facets [4] (e.g. “drug holidays” or inappropriate and irregular dosing time), five profiles should illustrate these different patient behaviours. The numerical simulations were performed at an individual level, using Mathematica software and led to several INR parameter results illustrating INR features during time. The main endpoint was the time during which the INR values were found outside the target zone (< 2 and > 4.5). 
Results: For a given profile of poor compliance simulated with a Markov regression model and supposing a once daily dose, the time duration (days) of an INR respectively > 4.5 was 18 + 15 for W and 12 + 8 for A (mean + 2SD). The duration of an INR and < 2 was 8 + 7.9 for W and 23 + 10 for A. Accordingly, supposing a twice daily dose, the corresponding time durations were 12 + 10 (W) and 0.7 + 1.7 (A) with an INR > 4.5, and 1 + 3 (W) and 6.2 + 5 (A) with an INR < 2. 
Discussion: Intuitively, the long half-life of warfarin could damp the consequences of non-compliance on the efficacy and safety of the treatment in a more efficient way than acenocoumarol which has a short half-life. However our results indicate that physicians should take into consideration each individual patient’s compliance profile and the underlying disease (with its own thrombotic or haemorrhagic risks) for the choice of the most appropriate anticoagulant agent (including its daily regimen), in order to optimize the INR equilibrium and consequently to decrease the risk of adverse events. 
References:
[1] Holford, N.H.G. ‘Clinical pharmacokinetics and pharmacodynamics of warfarin : understanding the dose-effect relationship.’ Clin Pharmacokinet 1986;11:483-504. 
[2] Dayneka, N.L., Garg, V., Jusko, W.J. ‘Comparison of four basic models of indirect pharmacodynamic responses.’ J Pharmacokinet Biopharm 1993;21:457-78. 
[3] Mismetti, P., Reynaud, J., Laporte-Simitsidis, S., Thijssen, H., Tardy-Poncet, B., Tardy, B., Buchmüller, A., Decousus, H. 'Pharmacokinetic and pharmacodynamic variations of acenocoumarol orally administered either once or twice daily in patients with deep vein thrombosis.' Fundam Clin Pharmacol 1998;12:631-635. 
[4] Urquhart J. ‘Role of patient compliance in clinical pharmacokinetics : a review of recent research.’ Clin Pharmacokinet 1994;27:202-215. 
[5] Boissel, J.P, Nony, P..'Using pharmacokinetic-pharmacodynamic relationships to predict the effect of poor compliance.' Clin Pharmacokinet 2002;41:1-6. 

Implications of Including and Excluding Correlation of Random Effects in Hierarchical Mixed Effects Pharmacokinetic Models

Nicholas H.G. Holford 1, Jogarao V.S. Gobburu,2 Diane R. Mould 3
1 Dept of Pharmacology & Clinical Pharmacology, University of Auckland, Private Bag 92019, Auckland, New Zealand, 2 Pharmacometrics, Division of Pharmaceutical Evaluation-1, Office of Clinical Pharmacology and Biopharmaceutics, Center for Drug Evaluation and Research, Food and Drug Administration, Rockville, MD 20852. 3 Projections Research Inc., Phoenixville, PA 19460
poster
Population modeling is increasingly being employed to make important decisions during drug development. Fundamentally, pharmacokinetic and pharmacodynamic parameters (e.g.: clearance, volume of distribution, maximal effect) are mutually independent. On the other hand, a common (initially unidentified) covariate could explain between subject variability in more than one parameter. Estimation of random correlation between parameters is controversial. To our knowledge, no systematic investigation of the influence of random correlation of parameter estimation has been reported. The present analysis was conducted to explore the consequences of including or excluding correlation terms in a population pharmacokinetic model. 1000 sparse (120 subjects, 4 observations/ subject) and dense data sets (30 subjects, 6 observations/subject) were simulated for an aminoglycoside drug given intravenously with or without correlation between clearance and volume of distribution. True and false models were fitted to the simulated data and bias and imprecision of the parameters were calculated. The bias and imprecision of true and alternate model parameters were within 20%. There is a high probability (80%) of correctly identifying the true model using the log-likelihood ratio test. Inclusion or exclusion of correlation of random effects using the log likelihood ratio test as the model selection criteria is reliable. False inclusion or exclusion of correlation of random effects is generally forgiving with respect to model selection and bias and imprecision of the parameter estimates but clearance estimates are not equivalent if correlation is ignored.

Modelling of drug absorption as a transport-limited process

Jan Freijer, Teun Post, Bart Ploeger, Joost DeJongh, Meindert Danhof
LAP&P Consultants, Leiden, The Netherlands
poster
Objectives: To explore the properties of an oral absorption model that considers the transport limitation between the sites of administration and absorption. The model is evaluated in the context of the mixed-effects approach. 
Introduction: Absorption of orally administered drugs from the GI tract is an important determinant of the onset of the drug effect. Not surprisingly, much emphasis is on modelling of the absorption process. Models of systemic drug absorption are frequently based on a direct or a delayed (lag time) first-order rate process. These models assume instantaneous presence of the drug in the absorption compartment and subsequently an exponential decrease of the absorption rate with time, thus implying an unrealistically sharp entrance front of the drug at the absorption site. In practice, the use of the first-order approach to predict plasma concentrations frequently yields a considerable mismatch between predicted and measured concentration profiles, particularly for the upswing of the plasma concentration after administration.
Methods: Weiss and co-workers [1] have proposed the Inverse Gaussian Density (IGD) input function as an alternative for the first-order absorption model to describe the absorption-time curve. Recent work [2-3] has shown that this type of absorption model can indeed adequately describe the upswing in the concentration-time curve when combined with compartmental pharmacokinetic (PK) models. Furthermore, from transport physics a mechanism is known that can explain the Inverse Gaussian shape of the absorption-time curve. The IGD absorption model was implemented in NONMEM to analyse the PK of two different drugs using data from various phase I trials. 
Results and conclusions: The appealing aspect of the IGD input function is that it contains just two parameters (transport velocity and dispersion length). Additionally, the parameter values can be translated into the appearance of the plasma concentration curves after single dose administration. The two parameters in this model, transport velocity and dispersion length seem to be related to the characteristics of GI tract passage and chemical properties of the drugs studied. It is concluded that the IGD input function is an absorption model that possesses promising properties for evaluating and optimising transport-limited absorption processes.
References
[1]Weiss, M (1996) A novel extravascular input function for the assessment of drug absorption in bioavailability studies. Pharmaceutical Research 13: 1547-1553.
[2]Higaki, K, Yamashita, S, Amidon, GL (2001). Time-dependent oral absorption models. Journal of Pharmacokinetics and Pharmacodynamics 28:109-128.
[3]Tatsunami, S, Sako, K, Kuwabara, R, Yamada, K (1998). Using Gaussian-like input rate function in the two-compartment model. Formulation and application to analysis of Didanosine plasma concentration in two Japanese hemophiliacs. Int.J.Clin.Pharm.Res. 18:129-135.

Optimal Designs For Parameter Estimation And Model Discrimination

T. Waterhouse (1), J. Eccleston (1), S. Duffull (2)
(1) School of Physical Sciences, University of Queensland, Australia; (2) School of Pharmacy, University of Queensland, Australia
poster
Introduction: The use of theoretical techniques for developing optimal designs for PKPD experiments has received some treatment in the pharmacology literature. Most of the work has been oriented toward designs that optimise the estimation of parameters for a specified, usually non-linear, model. A generalisation of this work has lead to the development of compound criteria for optimising designs for 2 or more proposed models [1]. In addition, criteria for discrimination between competing models has also been proposed [2] but has received very little treatment in the pharmacology literature. 
Objective: To investigate the utility of various criteria for optimising designs for parameter estimation and model discrimination for a number of competing models. 
Methods: The D-optimality criterion (det(I), where I is the information matrix) was used for assessing designs with respect to parameter estimation of a single model; a compound criterion (det(IM1)1/p1 x det(IM2)1/p2, where IM1 is the information matrix for model 1 and p1 is the number of parameters for model 1) was used for assessing designs for 2 or more models; and T-optimality for discrimination between models. The current work pertains to two competing PD models, the linear model and the Emax model. Four general methods for combining multiple criteria are assessed. 
1.	Maximise the compound criterion as defined above. 
2.	A sequential method, where the T-optimal design points are computed initially and then the compound D-optimal design points estimated conditional on the T-optimal design. 
3.	A joint criterion was developed that is the combination of the T-optimal and compound D-optimal criteria. 
4.	Simulated annealing is used to determine a class of designs that optimise all three criterion independently and simultaneously [3]. 
Results: The table below shows the marginal efficiencies of each design in terms of the linear model, the Emax model and model discrimination. A design which is optimal in terms of each of the 3 criteria does not exist. However, there is a small class of designs produced by method 4 which is at least 65% efficient in terms of the linear model, at least 90% efficient in terms of the Emax model, and least 85% efficient for the T-optimal criterion. This class of designs includes those found in the 3 previous methods. 
Method 	Efficiency 	
	Linear	Emax	T-optimality 	
1	67%	100%	86% 	
2	68%	92%	90% 	
3	68%	98%	89% 	
4	65%	90%	85% 	
Conclusion: The methods presented here offer an opportunity for experimenters to design experiments which are efficient with respect to parameter estimation and model discrimination over two and potentially more, competing models. This research is ongoing with investigations of joint criteria and modifications, and the consideration of more than two competing models. 
References:
[1] Walter, E. and Pronzato, L. (1997) Identification of Parametric Models. (Transl. John Norton) Chapter 6: Experiments. Springer, Masson, London.
[2] Atkinson, A.C. and Fedorov, V.V. (1975) The design of experiments for discriminating between two rival models. Biometrika 62(1):57-50.
[3] Eccleston, J. A. and Whitaker, D. (1999) Optimal change-over experiments using multi-objective simulated annealing. Statistics and Computing 9:37-42.

Clinical Trial Simulation of the Dose-Response Relationship of a Direct Thrombin Inhibitor, Dabigatran Etexilate, in Hip Replacement Patients

C. Garnett (1), K.H. Liesenfeld(2), C. Tillmann(2), I. Troconiz(3), H.G. Schaefer(2), J. Stangier(2), H. Lee (1)
(1) Center for Drug Development Science, Georgetown University, Washington, DC; (2) Boehringer Ingelheim Pharma GmbH & Co KG; (3) School of Pharmacy, University of Navarra, Pamplona, Spain
poster
Objectives: To estimate the posterior distribution of the maximum response (Rmax), the minimum response (Rmin), and the area under the response-time curve over 24 h (AURC24h) for the blood coagulation markers ECT and aPTT for 4 doses of dabigatran etexilate (50 mg bid, 150 mg bid, 225 mg bid, and 300 mg qd); and to calculate the power to detect differences in the PD parameters between the qd and the three bid dose groups.
Methods: The simulation platform consisted of a covariate distribution model; a PK model with covariates; PD models for ECT and aPTT; stochastic models for PK and PD parameter uncertainty, interindividual variability and residual error; and a nominal trial execution model consisting of 300 patients per dose group.  100 replications of the simulation model were performed using Trial Simulator(r).  PD parameters were calculated using model-independent techniques in S-Plus and analyzed with Dunnett's multiple simultaneous comparisons using the 300 mg qd dose as control. The power was calculated as the number of replicates showing p-value <0.05 between doses and its 95% CI was reported.
Results:  The simulated distributions of the covariates, concentrations, ECT, and aPTT were comparable to the observed clinical data. The geometric mean values of baseline-corrected AURC24h for ECT were 202, 614, 925, and 626 sec*h for the 50, 150, 225 mg bid and 300 mg qd dose groups, respectively, and the gCV% ranged from 65 to 73%. For aPTT, the geometric mean values of baseline-corrected AURC24h were 130, 317, 420, and 311 sec*h for the 50, 150, 225 mg bid and 300 mg qd dose groups, respectively, and gCV% ranged from 47 to 158%. Only 1% (95%CI=0-3%) of the replicates showed a significant difference between the 300 mg qd and 150 mg bid dose groups for AURC24h for ECT; similarly, power was 7% (95%CI=2-12%) for aPTT.  Rmax for the 300 mg qd dose was similar to the 225 mg bid dose for ECT (power = 17%, 95%CI=13-21%) and for aPTT (power = 12%, 95%CI=6-18%).  For both ECT and aPTT, Rmin for the 300 mg qd dose was higher than the 50 mg bid dose (power = 100% and 95%, respectively) and was lower than the 150 mg bid dose (power=100%, for both).
Conclusions:  These results suggest the 300 mg qd dose may be therapeutically equivalent to the bid doses. This inference may be tested by incorporating clinical outcome models for deep vein thrombosis and major bleeding into this clinical trial simulation model.

Population PK-PD analysis of cardiovascular effects of non-cardiovascular drugs with the emphasis on QT prolongation

Vladimir Piotrovsky
Advanced PK-PD Modeling and Simulation, Johnson & Johnson Pharmaceutical R&D, Beerse, Belgium
poster
Non-cardiovascular drugs may exhibit effects on biomarkers known as vital signs, like heart rate (HR), blood pressure (BP), electrocadiogram (ECG), etc., that limits the drug dose and sometimes even results in the drug development failure. Particularly, the prolongation of the QT interval may cause a potentially fatal arrhythmia known as torsade de pointes. From the point of view of data analysis, vital signs have common properties: high inter- and intraindividual variability, diurnal rhythm, substantial gender differences. Moreover, at multiple administration, a tolerance to drug effects may develop resulting in a decrease in its magnitude.
Having this similarity in mind, the following operational model can be used for "simple" biomarkers (HR, BP, but not QT):
Y = BSL * (1 + DIURNAL + DRUG.EFF) + ERR
where BSL is the "true" baseline value of the variable Y; DIURNAL and DRUG.EFF are the diurnal variability and drug effect component of the model, respectively; ERR is the residual error. DIURNAL and DRUG.EFF are expressed in terms of changes relative to the baseline value. "True" baseline means it corresponds to zero values of DIURNAL and DRUF.EFF, and this does not necessarily coinsides with the predose level of Y. The drug concentration (in plasma or "effect-compartment") enters DRUG.EFF in the form of Hill equation or other suitable PD model, which can also include a tolerance
In case of the QT interval, the above model should be updated with a term describing the intrinsic dependence of QT on RR interval:
QT = BSL * (CORR + DIURNAL + DRUG.EFF) + ERR
where a "correction" term CORR adapts QT according to changes in RR. The latter may change due to physical activity, diurnal rhythm, drug effects, and at random. Proper correction is a key issue in evaluating drug effects on QT interval. A conventional approach is based on an assumption of universal correction for all individuals. This contradicts, however, to recent findings [1]. 
The model is suggested, which uncludes the power correction formula with the exponent parameter subject to interindividual variability. This is implemented via mixed effects. DIURNAL and DRUF.EFF are implemented using bi-cosine and Hill function, respectively. Examples of drugs exhibiting significant QT prolongation and those having negligible/limited effect are given.
References
[1] Malik M., Camm AJ. Drug Safety 2001, 24:323-351.

Improved Computational Methods for Statistically Consistent and Efficient PK/PD Population Analysis

Robert Leary [1], Roger Jelliffe [2], Alan Schumitzky[2], Michael Van Guilder [2]
[1] San Diego Supercomputer Center, University Of California, San Diego [2] Laboratory Of Applied Pharmacokinetics, USC School Of Medicine, Los Angeles
poster
Objectives: Most current PK/PD population analysis methodologies are based on parametric maximum likelihood estimators that use approximations such as FO, FOCE, and Laplace in the parametric likelihood function to reduce computational effort. Such approximations can severely compromise statistical quality in terms of both statistical consistency (bias) and statistical efficiency. Nonparametric (NP) maximum likelihood methods use exact likelihood functions but require the solution of a much higher dimensional likelihood optimization problem. Here we investigate an NP algorithm which uses principles of optimal design to decompose this high-dimensional problem into a sequence of low dimensional problems that can be easily solved numerically.
Methods: The nonparametric adaptive grid (NPAG) PK/PD population analysis program developed by our laboratory was modified to replace the local grid refinement strategy at each iteration with an optimization over the relatively low-dimensional PK/PD model parameter space to identify coordinates of new support points to introduce at each successive iteration. The form of this optimization problem is defined by the Fedorov optimal design methodology [1] applied to the convex NP maximum likelihood problem.
Results: NPOD (NP optimal design) strongly outperformed NPAG in terms of computational efficiency in comparative nonparametric analyses, often with 10-fold or greater speedups. For example, on a small nonlinear 3-compartment model with 19 subjects, NPOD reached the same optimal solution as NPAG in 10 vs. 180 minutes on a current generation PC. A large 641-subject model was converged in 1.5 days with NPOD as opposed to over 2 weeks with NPAG. When tested against PEM, a new consistent parametric analysis program developed by our laboratory, NPOD achieved comparable statistical efficiency at significantly lower computational expense.
Conclusion: The NPOD methodology is computationally much more efficient than NPAG. It can be used both for parametric and NP analyses to provide statistically efficient and consistent estimators by avoiding the likelihood approximations that degrade the statistical performance of other methods.
Reference:
[1] Fedorov, V.V: Theory of Optimal Experiments, translated and edited by W.J. Studden and E.M. Klimko, New York: Academic Press, 1972.

Population pharmacodynamic analysis of the anticonvulsant effects of tiagabine and lamotrigine in combination

Daniël M. Jonker (1,2), Rob A. Voskuyl (1,2) and Meindert Danhof (1)
(1) Leiden/Amsterdam Center for Drug Research, Division of Pharmacology, Gorlaeus Laboratories, Leiden, The Netherlands; (2) Stichting Epilepsie Instellingen Nederland, Heemstede, The Netherlands
poster
Objective: Characterization of the pharmacodynamic interaction between the antiepileptic drugs tiagabine and lamotrigine on basis of the anticonvulsant effect in the cortical stimulation model in the rat.
Methods: The study was conducted according to a partial cross-over design, in which the plasma concentrations of both drugs were increased linearly in the absence and presence of a steady-state concentration of the second drug. The anticonvulsant effect was quantified by counts of 4 specific ictal signs (eye closure, forelimb clonus, forelimb extension and head jerk). These counts were related to the total plasma concentrations of both drugs with an inhibitory sigmoid model that was based on the density function for a Poisson distribution. This population model was implemented in NONMEM using the Laplacian method with the likelihood option. For each ictal sign, the tiagabine-lamotrigine interaction was assessed by response surface analysis based on a parametric interaction model [1].
Results: When given separately, both tiagabine and lamotrigine suppressed all ictal signs in a concentration-dependent manner, with the exception of eye closure, which was not suppressed by lamotrigine. The response surface analysis showed that the pharmacodynamic interaction between tiagabine and lamotrigine was synergistic for the ictal signs eye closure and head jerk. In contrast, the interaction was additive for the ictal signs forelimb clonus and forelimb tonus. These results were visualized by plotting the difference between the observed effect and the additive effect, showing that synergy for eye closure and head jerk was maximal at concentrations near the EC50 values of both drugs.
Conclusion: These findings show that the nature and magnitude of the pharmacodynamic interaction between tiagabine and lamotrigine differs between specific motor components of epileptic seizures.
Reference:
[1] Minto CF, Schnider TW, Short TG, et al. Response surface model for anesthetic drug interactions. Anesthesiology 2000;92:1603-1616.

Comparison of NONMEM with the Two-Stage approach for obtaining population means of the pharmacokinetic parameters of fluoxetine

D.M. Reith (1), W. Hooper (2), M Franklin (2).
(1) Dunedin School of Medicine, University of Otago, Dunedin, New Zealand; (2) Q-Pharm Pty Limited, Queensland Institute of Medical Research, Brisbane, Australia
poster
Objectives: NONMEM has been validated primarily using simulated datasets and there are relatively few studies comparing the two-stage and population approaches using real patient or volunteer data.  The aim of the present study was to compare the two approaches using a large dataset accumulated during the conduct of bioequivalence studies.  
Methods: One hundred volunteers were observed to ingest 40 mg of the same formulation of fluoxetine.  Each subject had 19 plasma samples collected between time 0 and 26 days post-dose.  Plasma fluoxetine and norfluoxetine levels were determined using a GC-MS assay.  The two-stage approach was used to determine Ka and Ke for each subject by nonlinear curve fitting using WinNonLin(tm) and Ke for each subject by fitting the terminal elimination phase using Stemkinetics(tm) and Stata , and the mean values were determined for the 100 volunteers.  A one compartment, first order absorption and elimination model (ADVAN2) was used to determine Ka and Ke using NONMEM and first order conditional estimation.  The POSTHOC command was used to provide individual estimates of Ka and Ke to determine if NONMEM can detect a bimodal distribution of Ke.  Starting with all 19 observations per subject, and randomly removing one observation per subject at each step, Ka and Ke were determined for the reduced datasets.  
Results: NONMEM estimated similar values for Ka and Ke to the two-stage approach down to three observations per subject.  The CV% for ETA1, ETA2 and EPS were acceptable (< 30%) down to 2 observations per subject.  There was no deterioration in the precision or bias of the models with the progressive reduction in observations.  Posthoc estimates of Ke were normally distributed rather than demonstrating the bimodal distribution of Ke from the two-stage approach.  NONMEM and WinNonLin determined similar estimates for Ke and Ka.  Stemkinetics(tm) and Stata  determined similar estimates of Ke to each other but differed to the two other programs.  
Conclusions: NONMEM produced acceptable estimates of the pharmacokinetic parameters when there were three or more observations per volunteer but, in contrast to the two-stage approach, did not detect the bimodal distribution of the Ke for fluoxetine.

Integrated population pharmacokinetic model of both cyclophosphamide and thiotepa suggesting a mutual drug-drug interaction.

Milly E de Jonge(1), Alwin DR Huitema(1), Sjoerd Rodenhuis(2) and Jos H Beijnen(1).
(1) Department of Pharmacy and Pharmacology, The Netherlands Cancer Institute/Slotervaart Hospital, Louwesweg 6, 1066 EC, Amsterdam, The Netherlands. (2) Department of Medical Oncology, The Netherlands Cancer Institute, Plesmanlaan 121, 1066 CX, Amsterdam, The Netherlands.
poster
Aim: Cyclophosphamide (CP) and thiotepa (TT) are frequently administered simultaneously in high-dose chemotherapy regimens. The prodrug CP shows strong autoinduction resulting in increased formation of its activated metabolite 4-hydroxycyclophosphamide (4OHCP). TT was shown to inhibit this activation of CP [1]. Recently we suggested that CP may also induce metabolism of TT to its metabolite tepa. The aim of the current study was to investigate whether the latter newly recognized interaction could be described with a mechanistic population pharmacokinetic model of sequentially administered CP and TT including their active metabolites 4OHCP and tepa, respectively. 
Methods: Plasma samples were collected from 50 patients receiving 87 courses of a combination of high-dose CP (6000 or 4000 mg/m2), TT (480 or 320 mg/m2) and carboplatin (1600 or 1067 mg/m2) given in short infusions during 4 consecutive days. For each patient, approximately 20 plasma samples were available per course. Concentrations of CP, 4OHCP, TT and tepa were determined using GC and HPLC. Kinetic data were processed using the nonlinear mixed effect modeling program NONMEM with log transformed data and the first order (FO) method. For several parameters both interindividual variability (IIV) and interoccasion variability (IOV) were estimated.
Results: The pharmacokinetics of TT, tepa and CP were described with a two-compartment model and those of 4OHCP with a one-compartment model. Both CP and TT were eliminated with a non-inducible and an inducible pathway, the latter resulting in formation of 4OHCP and tepa, respectively (ClindTT= 16.0 L/h, Clnon-indTT=16.8 L/h, ClindCP= 2.9 L/h, Clnon-indCP=2.3 L/h, VTT=45.6 L, Vtepa=13.5 L, VCP=37.6 L, V4OHCP=1 FIX). Induction of CP and TT metabolism was mediated by two hypothetical amounts of enzyme whose quantities were increased with time in the presence of CP. The amount of enzyme involved in CP metabolism increased with a zero-order rate constant of 0.024 h-1, and the one involved in TT metabolism followed a zero order formation with a decrease of the first order elimination rate constant (Kenz=0.034 h-1). Interindividual variabilities on the enzyme formation rate constants were rather large, 43% and 240% for those involved in CP and TT metabolism, respectively. Inhibition of CP autoinduction by TT was modeled as a reversible, non-competitive, concentration-TT-dependent deactivation reaction. The elimination rate constants of tepa and 4OHCP were 0.6 h-1 and 136 h-1, respectively.
Conclusion: The developed mechanism-based enzyme model successfully described the complex pharmacokinetics of CP and TT given in combination. The model confirmed induction of TT metabolism and it is obvious to assume that CP is responsible for this phenomenon by increasing the amount of enzyme involved. The existence of a mutual pharmacokinetic interaction between CP and TT may be relevant in clinical practice. 
[1] Huitema ADR, Mathot RAA, Tibben MM et al. A mechanism-based pharmacokinetic model for the cytochrome P450 drug-drug interaction between cyclophosphamide and thioTEPA and the autoinduction of cyclophosphamide. J Pharmacokinet Pharmacodyn 2001; 28: 211-30.

Population Pharmacokinetics of onercept in healthy subjects.

Sophie Glatt, Mauro Buraglio, Eliane Fuseau
Emf-consulting and Serono
poster
Purpose: To develop a population pharmacokinetic (POPPK) model and to determine the covariates affecting the pharmacokinetics of onercept (recombinant human tumour necrosis factor binding protein-1) in healthy subjects.
Methods: Onercept PK data were obtained from 36 healthy male and female subjects (3 phase I studies). In study 1, 12 subjects received increasing single intravenous doses of 5, 15, 50, and 150 mg onercept. In study 2, 12 subjects received single intravenous (IV), subcutaneous (SC) and intramuscular (IM) doses of 50 mg onercept. Study 3 investigated the pharmacokinetics of onercept following repeat SC administration of 6 doses of 50 mg every 48h in 12 subjects.
NONMEM was used to build a base model while the final model was determined after the covariates selection.
Results: The disposition of onercept could be described using a two- compartment model with two absorption processes: a first order followed by a zero order. Slow absorption following SC and IM dosing was observed and suggested that the absorption was the rate limiting process. The population mean (CV%) values for clearance (CL), absorption rate constant (KA), duration of the zero order process (D) and bioavailability (F) were 3.86 L/h (4.4%), 0.0427 h-1 (4.1%), 46.5 h (0.4%) and 0.812 (5.7%), respectively. The population analysis indicates that the variability in CL is moderate. The final estimate of the volume of distribution of the central compartment (Vc) was close to the plasma volume.
The only significant covariate was found to be the sex, which affected the absorption lag time (on the duration of the zero order process) and suggested 25% longer values in male subjects. 
Conclusion: The proposed model characterizes well the overall pharmacokinetics profile of onercept after IM, SC and IV administration. The pharmacokinetics of onercept showed limited intersubject variability and appeared not to be affected by the covariates tested, which included demographic parameters and laboratory values. The apparently longer absorption lag time observed in male subjects cannot be explained physiologically, is unlikely to have any clinical relevance and is more likely an artifact of the analysis.

Comparing binary tree and automated machine learning covariate search strategies

Robert Bies (1,2), Mark E. Sale (3), Bruce G. Pollock (1,2)
(1)Department of Pharmaceutical Sciences, School of Pharmacy, (2) Department of Psychiatry, Western Psychiatric Institute and Clinic, University of Pittsburgh, Pittsburgh, PA (3)Glaxo Smith Kline, North Carolina, USA
poster
Covariate search strategies have provided some measure of controversy with respect to the identification of significant or correlated effects. Using a dataset of 58 subjects administered IV citalopram infusion with intensive plasma concentration sampling, two covariate search strategies were undertaken. The first was a stepwise covariate search, employing both forward addition/backward removal and backward removal/forward addition directions under both First Order and First Order Conditional estimation conditions. The second was an automated covariate search strategies employing a genetic algorithm approach under the first order estimation condition. All covariate searches were carried out using NONMEM. A two-compartment model was used to describe citalopram pharmacokinetics after IV administration. The covariates age, weight and sex were evaluated on each of the parameters CL, Q, V1 and V2. The genetic algorithm approach may evaluate the search space identifying effects that are only present when in combination. Results from the binary tree approach yielded different models depending on the search direction and order. The genetic algorithm search resulted in yet a different model evaluated with a lower objective function (under first order estimation conditions). The genetic algorithm search was sensitive to the number of individual models specified per generation (individual=model). Searches with smaller numbers of individuals resulted in the identification of an optimal region of solutions. As the numbers of individuals increased a single optimal solution was detected. The model identified with the GA approach had the lowest objective function detected (D30, Dq=+2, Dh=-2 relative to the best model found with the stepwise approach). The final model from the GA method identified two inter-individual variability terms and incorporated all three covariates (sex, weight and age) on clearance and two covariates (clearance and sex) on V2 into the model.

D-Optimal Design for Multivariate Response: Prospective Planning of a Beta-blocker Study in Rat Involving Cassette Dosing

I. Gueorguieva, L. Aarons, T. Rodgers and M. Rowland
Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, University of Manchester, U.K.
poster
Objective: To suggest optimal sampling times for an iv bolus experiment to study the tissue disposition kinetics of eight beta-blockers in rat.
Methods: A tissue perfusion-rate limited whole body physiologically based (WBPBPK) model was assumed to predict beta-blocker disposition. We aim to plan experiments for efficient estimation of drug- dependent parameters (tissue-to-blood partition coefficients) by employing a D- optimal design criterion. This criterion minimises the volume of the joint confidence region by maximising the determinant of the Fisher information matrix (FIM) (inverse of variance-covariance matrix). It was further assumed that measurements made at distinct times are independent, but measurements made of each drug tissue concentrations are correlated with a constant variance- covariance matrix. These variance-covariance matrices of response for two of the eight beta-blockers were available from a previous iv bolus study. Initial parameter estimates were also obtained from a previous experiment carried out under steady-state conditions. As the assumptions for homoscedasticity and normality of the residuals are often violated in mechanistic models this was taken into account when designing the experiment. In this multivariate response (WBPBPK) model, model parameters were shared between response components. Additionally, the beta-blockers are intended to be cassette dosed and hence the same design needs to be applied to all the drugs in the same cassette. This leads to a compromise design among the separate drug's optimal sampling times. To determine the D-optimal design the determinant of the FIM has to be maximised over the whole design space. Unfortunately the surface of this determinant is very convoluted which places additional requirements on any optimiser. The selection of an appropriate optimiser involved comparison of the performances of several optimisation methods (downhill simplex, simulated annealing, adaptive random search, Fedorov) to a number of simpler pharmacokinetic models, including a multivariate response for a parent drug and metabolite.
Results: A hybrid scheme consisting of simulated annealing followed by downhill simplex performed the most consistently well. Using this optimisation procedure D-optimal sampling times for each of the beta-blockers were obtained. These were compared to several practically feasible designs and D-efficiency was computed. Average efficiencies of the cassette for each of the practical designs were compared. Based on that, the most efficient design was suggested for implementation.
Conclusions: The proposed hybrid optimisation scheme, although involving high computational costs, proved to be a robust and efficient approach.This technique for multivariate response optimal design can be readily implemented in other similar situations, such as parent drug and metabolites and pharmacokinetic/pharmacodynamic models.
References: Draper and Hunter (1966) Biometrika 53: 525- 533.
Corana (1987) ACM Transactions on mathematical software 13(3): 262-280. 

Development of a dosing strategy for enoxaparin in patients with renal impairment using a population pharmacokinetic approach

Bruce Green(1), John Atherton(2), Justin Westhuyzen(2),Leeanne Kluver(2),David Saltisi(2)
(1) School of Pharmacy, University of Queensland, Australia, (2) Royal Brisbane Hospital, Queensland, Australia
poster
Background: A dose adjustment strategy for enoxaparin in patients with renal impairment has recently been added to the product label in Australia. The recommendation is 100 IU/kg twice daily if estimated glomerular filtration rate (GFR) is >30ml/min, and 100 IU/kg daily if GFR is equal to or below this value. It is not known what impact this dosing strategy has on concentration time profiles of enoxaparin. 
Aim:To undertake a population pharmacokinetic study to determine a suitable dosing strategy for patients with varying degrees of renal impairment.
Methods: Patients admitted to the Royal Brisbane Hospital with Acute Coronary Syndrome were eligible for enrolment in the study. Patients recruited had varying degrees of renal function, and administered doses of enoxaparin ranged from 50 to 100 IU/kg (100 IU = 1mg) twice daily according to current guidelines. Approximately 10 blood samples to determine anti Xa concentration were taken per patient. A population pharmacokinetic model to describe the data was developed using FOCE with INTERACTION in NONMEM (version 5). Estimates of renal and non renal clearance were used to develop a dosing strategy for patients with varying degrees of renal function. This dosing strategy was tested by simulating a concentration time profile using the final covariate model in NONMEM. One hundred bootstrapped datasets were simulated. The optimal dose model was defined as that which could rapidly achieve the desired enoxaparin concentration range of 500 to 1000 IU/L.
Results: Thirty-five patients were recruited in the study with an estimated glomerular filtration rate (GFR) that ranged from 17 to 92 ml/min. A two compartment first order input model with log normal between subject variability (BSV) on clearance (CL), central volume compartment (Vc) and basal anti Xa activity, with additive and proportional residual variance was found to be the most suitable baseline structural model. The final covariate model included estimated GFR on CL according to the method described by Cockroft and Gault but where ideal body weight was used as the weight descriptor. The central volume compartment Vc was best described by total body weight. Fraction excreted unchanged was estimated at 75% and total clearance described by:
Total CL (L/hr) = 0.681/4.80 * (GFR) + 0.229
Using simulation experiments, the variable dosing regimen determined from the above equation appeared to predict desirable enoxaparin concentrations between 500 and 1000 IU/L after 7 days. A loading dose strategy of 100 IU/kg twice daily for 3 days, followed by an individualised dosing strategy dependent upon renal function appeared optimal. Simulations using manufacturer dosing guidelines did not appear to attain efficacious concentrations for those with an estimated GFR <30ml/min. Those above 30ml/min appeared satisfactory for the first three days, although accumulation appeared to occur thereafter. 
Conclusions: Current dose guidelines for enoxaparin in patients with renal impairment do not seem to result in a desirable concentration time profile of 500 to 1000 IU/L. This appears rapidly achievable by giving 100 IU/kg twice daily for 3 days, then dose individualising based on renal function.

Incorporating Variability in WBPBPK Models: Application to Three Benzodiazepines with Extrapolation from Rat to Man

S. Gisbert, I. Gueorguieva, L. Aarons and M. Rowland
. Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, University of Manchester, England.
poster
Aim:Previously we developed a WBPBPK (Whole Body Physiologically Based Pharmacokinetic) model for diazepam in rat incorporating variability in drug dependant parameters (clearance, coefficients of partition: Kp) as well as in drug independant parameters (physiological parameters: volumes, blood flows) which was used for extrapolation to man. The aim of the present work was to extend the WBPBPK model developed for diazepam (DZ) to two other benzodiazepines: flunitrazepam (FZ) and midazolam (MZ). For each of these three molecules we used the models to investigate the impact of different values of intrinsic clearance (from the literature, from human PK data and from in vitro studies).
Materials:In vivo studies in rats: The drugs were administered i.v. to each of 24 male Sprague-Dawley rats at a dose of 1 and 2 mg/kg. In vivo studies in man: iv PK data provided by Hoffman-La Roche. In vitro studies in man: Human liver microsomes were isolated from sections of 12 individual humans livers. Clearances for DZ and MZ were determined via substrate depletion and for FZ via metabolite formation. Studies with testosterone were performed to study the activation of CYP3A4(1).
Methods:Modelling of rat and man plasma data to obtain estimates of the total clearances was performed in NONMEM using bi and three exponentials. Due to limited renal excretion total clearance was assumed equal to hepatic clearance. Using the well-stirred model estimates of the intrinsic clearance for the drugs were obtained.Optimisation of the Kp values of the PBPK model was performed using MATLAB 6.1. Using weighted least squares the obtained Kp values were used for susequent simulations in rat and man.
Results and Discussion:Physiological variability contributed considerably to the overall variability particularly at early times. At later times variability was determined by intrinsic clearance. The quality of the predictions was highly dependent on the population estimate of intrinsic clearance used in the simulations. Failure to adequately account for both variability in physilogical and drug dependent parameters compromises the ability to predict PK variability in man from in vitro and animal tissue data. 
References:(1) Heteroactivation of CYP3A4 substrates: Impact of intrinsic clearance and interindividual variability. H.C. Rawden A. Tindall, D. Hallifax, B. Houston (2001) Drug Metabolism Review 33(1):211. 

Multiple Imputation of Serum Creatinine

In-Sun Nam and Leon Aarons
University of Manchester
poster
For many drugs that are excreted renally, dosage regimens are often adjusted for renal function. Serum creatinine concentration is the most widely used measure of glomerular filtration rate (GFR) which itself is the most commonly used index of renal function. There are more accurate measures of GFR, such as creatinine clearance (CL) and especially, iothalamate CL, inulin CL, or iohexol CL, but these involve considerable practical problems. Several formulae relating plasma creatinine level to creatinine clearance exist, of which the most widely used formula is due to Cockcroft-Gault [1]. Since serum creatinine and creatinine CL were potentially important covariates related to the CL in a particular drug modelling exercise, alternative ways of imputing missing values other than the carry-forward method were investigated, as the latter was likely to introduce bias into the estimates of interest and their standard errors, and therefore cause an impact on various hypothesis tests [2]. Moreover, the proportion of missing data was too great in the dataset of interest for whole cases to be deleted.
The two major classes of modern missing data procedures are multiple imputation and maximum likelihood, and they are likely to yield almost identical results if the two are utilised in comparable ways [3], because they are derived from similar theoretical foundations. Firstly the two methods are generally fully parametric, utilising joint probability models for the observed and missing data, and secondly missing values are viewed as a cause of random variation to be averaged over. Of the two methods, multiple imputation has been widely used in the behavioural, biomedical, and social sciences, due to increased access to new computational methods and tools [4].
Considering the half-life of creatinine and reported autocorrelation between successive levels, especially due to its dependence of meat consumption, a continuous first order autoregressive multiple imputation model which was a non-explosive model satisfying the stationarity constraint, was originally utilised to describe the dependency between any two time-adjacent serum creatinine values. It was suggested that the slope of the reciprocal of serum creatinine versus time did not permit an accurate assessment of the progression rate of renal disease [5]. Nonetheless, due to practical difficulties, a simultaneous PK analysis of the specific example dataset was performed with serum creatinine imputations using a simpler model structure with weighted means of observed serum creatinine levels. Throughout, a Bayesian approach was taken with implementation via Markov chain Monte Carlo methods. The results were compared with mean imputation and the carrying-forward methods. Our method closely resembles the error in variable approach taken by Bennett et al. [6].
References
[1] Cockcroft, D. W. and Gault, M. H. Prediction of creatinine clearance from serum creatinine. Nephron, 16:31-41, 1976.
[2] Little, R. J. A. and Rubin, D. B. Statistical Analysis with Missing Data. John Wiley, New York, 1987.
[3] Collins, L. M., Schafer, J. L. and Kam, C. A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychol. Meth., 6:330-351, 2001.
[4] Schafer, J. L. Multiple imputation: A primer. Stat. Meth. Med. Res., 8:3-15, 1999.
[5] Levey, A. S., Perrone, R. D. and Madias, N. E. Serum creatinine and renal function. Ann. Rev. Med., 39:465-490, 1988.
[6] Bennett, J. and Wakefield, J. Errors-in-variables in joint population pharmacokinetic/pharmacodynamic modeling. Biometrics, 57:803-812, 2001.

Sample Size Calculation based on Confidence interval for Pharmacokinetic Studies

K.Ogungbenro and L. Aarons
Centre for Applied Pharmacokinetics Research, School of Pharmacy and Pharmaceutical Sciences University of Manchester, Manchester, United Kingdom
poster
An important consideration in applied science studies such as clinical trials is the number of subjects to be included in the study. Since sample size is often proportional to the cost and power of the study, attempts are always made to include the minimum number of subjects in the study to balance the two effects. The Population pharmacokinetic approach has been widely used in drug development and the accuracy and the precision with which the parameters are estimated have been shown to depend on a number of design factors, including the sample size. To the best of our knowledge no analytical method has been applied to calculate the number of subjects required for these kind of studies. The use of likelihood ratio tests (with simulation) has been used to determine the number of subjects required for pharmacokinetic studies designed to detect the difference(s) in parameter(s) between two groups(1). 
This study focused on the use of a confidence interval (by simulation) approach to determine sample size for pharmacokinetic studies that are not necessarily designed to detect the difference between two groups. Much has been said about over-reliance on hypothesis testing in reporting experimental results and this is partly due to the availability of sample size methods for such studies. Beal (1989) and Grieve (1991) proposed a method based on confidence intervals for calculating sample size for experiments. The proposed method for pharmacokinetic studies involves using simulation to estimate the power of a particular design by estimating the confidence interval around a parameter of choice in the model to a particular level of precision. The method was applied to a one compartment first order absorption model and operating characteristics curves were generated for the different levels of precision for the clearance parameter.
References:
1. P.I.D. Lee, Design and Power of a population Pharmacokinetics Study, Pharmaceutical Research, 18: 75-82 (2001). 
2. S.L. Beal, Sample Size Determination for Confidence Interval on the population Mean and on the Difference Between Two Population Means, Biometrics, 45: 969-977 (1989). 
3. A. P. Grieve, Reader Reaction, Confidence Interval and Sample Sizes, Biometrics, 47:1597-1603 (1991). 

Non-Linear Mixed-Effects Models in NLME with Differential Equations

Christoffer W. Tornøe(1), Henrik Agersø(1), E. Niclas Jonsson(2), Henrik Madsen(3), and Henrik A. Nielsen(3)
(1)Clinical Pharmacology and Experimental Medicine, Ferring Pharmaceuticals; (2)Department of Pharmaceutical Biosciences, Uppsala University; (3)Informatics and Mathematical Modelling, Technical University of Denmark
poster
Objectives: The aim of the present analysis was to explore the possibility of implementing differential equations in the non-linear mixed-effects library NLME using an ordinary differential equation (ODE) solver with simultaneous sensitivity analysis.
Methods: The odesolve package [1] which can handle stiff and non-stiff systems of first-order ODE's was used in combination with NLME for parameter estimation in non-linear mixed-effects models. The gradient matrix was calculated by simultaneous solution of the system of ODE's in Eq.(1) and the corresponding first-order parametric sensitivity equations in Eq.(2).

­­­­­ Eq.(1) ­ dy/dt = f(y,t,p) 
­­­­­ Eq.(2) ­ dS/dt = JAC S + df/dp

where y and t are the dependent and independent variable, respectively, f is the structural model and p is a vector of fixed-effects parameters. S is the gradient matrix dy/dp, JAC is the jacobian matrix df/dy, and df/dp is a matrix of partial derivatives. The sensitivity equations were included in order to investigate whether they increase the numerical stability and the rate of convergence of the algorithm compared with numerical calculation of the gradient matrix.
Results: The pharmacokinetic (PK) data of the anti-asthmatic drug Theophylline was used to validate the proposed method. These data were reported and analyzed in Boeckmann et al. [2] and Pinheiro et al. [3] using a one-compartment pharmacokinetic model with first-order absorption and elimination. The proposed algorithm with and without sensitivity equations was numerical stable and the parameter estimates and predictive performance were accurate and comparable with results obtained from NONMEM and the SSfol function distributed with NLME.
Conclusion: The implementation of ODE's in the non-linear mixed-effects library NLME makes it a promising tool for population PK/PD analysis of complicated systems which cannot be solved analytically. The proposed algorithm can easily be extended to include other PK models as well as indirect response models for analysis of PD data.
References:
[1] Setzer, R.W. (2003). The odesolve package. http://cran.us.r-project.org.
[2] Boeckmann, A.J., Sheiner, L.B., Beal, S.L. (1994). NONMEM Users Guide - Part V, NONMEM Project Group, University of California, San Francisco.
[3] Pinheiro, J., Bates, D. (2000). Mixed-effects in S and S-PLUS, Springer-Verlag.

Population Pharmacokinetics of Vancomycin during Extra Corporeal Membrane Oxygenation (ECMO)

Hussain Mulla, Suneel Pooboni, David Jenkins, Graham Lawson, Richard Firmin, David Upton
Glenfield Hospital, Leicester
poster
Objectives: Extracorporeal membrane oxygenation (ECMO) is a life support system used in the treatment of severe respiratory or cardiorespiratory failure. Drug disposition is known to be altered during ECMO. Thus, the objective of this study was to determine population pharmacokinetics (POPPK) of vancomycin and their variability during ECMO. The study group included term neonates (0-1 month, n=15), older children (1 month-18 years, n=12) and adults (>18 years, n=18). 
Methods: The study utilised both prospective rich and retrospective scant data. A POPPK model was developed using WinNonMix (Version 2.0.1) from a total of 366 plasma observations from 45 patients. Vancomycin doses were based on age and renal function, ranging 10-15mg.kg-1 8-24 hourly. Prospective samples were drawn at baseline and then 30, 60,90, 120, 180, 240, 300, 360 and 420 mins post infusion. Steady state, scant data were obtained retrospectively from an assay database, cross-referencing with the patients medical records. 
Results: Mean (range) serum creatinine (SCr) levels were significantly higher amongst adults (125.1(48.3-224.5)), compared to neonates and older children (79.6(39-180) and 73.5 (26.5-158.9) μmol/L respectively), reflecting age and severity of illness. Data was examined using a two compartment model with an additive and proportional residual error. Exploration of covariates (following inclusion of weight) revealed correlations: SCr and age with CLC; age with VC. Significant improvement in model fit was observed when CLC was modelled as a non-linear function of SCr, and linearly associated with age up to 1000 days. The influence of age on VC was included into the model as a dichotomous variable (breakpoint 4000 days). The final population model was: CLC(age <1000 days) = 2.4 + 0.0018*Age (days) / Scr (μmol/L) L/kg/hr; CLC (age >1000 days) = 4.3 / Scr (μmol/L) L/kg/hr; CLi = 0.09L/kg/hr; VC (age < 4000 days) =0.45L/kg; VC(age > 4000 days) = 0.36L/kg; VT = 0.25L/kg. Interpatient coefficient of variation in CLC, CLi, VC and VT were 25.2%, 91%, 25.2% and 47.6% respectively, whilst residual error corresponded to a proportional error of 11.8% and additive error of 2.1mg/L. A validation data set showed the model to have a bias, -7.7% and precision, 26.7%. 
Conclusions: The results show significantly reduced clearance and expanded volume (Vss) in ECMO compared to previous reports in non-ECMO patients of similar ages. The results reflect expansion of blood volume during ECMO. 

Pharmacokinetic model for vancomycin performed with sparse data on neonates

Pascal Chanu (1), Audrey Janoly-Dumenil (2), Nathalie Bleyzac (2), Jacques Bourgeois (3), Brigitte Tranchand (1)
(1) Centre Léon Bérard; (2) Pharmacy-Hôpital Debrousse; (3) Neonatalogy unit-Hôpital Debrousse
poster
Objectives: The marked inter- and intra patient variability of the pharmacokinetics of numerous antibiotics is well known, especially in neonates. Moreover, we can presuppose that there is, at some extent, some degree of variability in effect during vancomycin therapy and that this variability is in some fashion related to plasma levels and to the administered dose of drug. In the present study, we tried to perform modelling of vancomycin, by using covariates on a large cohort in order to reduce inter- and intra patient variability. Indeed, it would be useful to predict pharmacokinetic parameters, clearance (Cl) and volume of distribution (Vd) of central compartment, in order to individualize dosage regimen with minimal disturbance to the neonates. 
Patients and Methods: Sparse data from 145 courses of vancomycin upon neonates up to one month old were recorded. Each treatment consisted in either a continuous 24 hour infusion (96 patients) or in a 2 hour infusion of vancomycin three times per day (49 patients). The mean number of samples per patient was 1.8 and ranged from 1 to 5 samples. Vancomycin was assayed by an immuno - enzymatic method (EMIT). Covariates collected were body weight (Bw) (range [0.52 ; 5] kg), post conceptional age (Apc) (range [26.4 ; 55.3] weeks), sex (M=1, W=2, ratio M/F = 1.13), creatinin clearance (ClCr) (range : [4.3 ; 59.3] ml.min-1/1.73 m²) and height (range : [29.5 ; 60] cm). Data analysis was performed using NONMEM version 5 under Visual-NM. 
Results: The best model for vancomycin was a two-compartment model associated to an additive error model (ADVAN 3 TRANS 4). The significant covariates were Apc and Bw for clearance and Bw for volume of distribution. The objective function decreased from 1474 to 1238 after inclusion of these covariates and variability in clearance decreased from 86% to 43%. 
Conclusion: Such a population model could allow physicians to predict pharmacokinetic parameters (Cl and Vd) and thus to prescribe a priori amounts of vancomycin for neonates with more safety and more efficiency.

Pharmacokinetics of cyclosporine in lung transplant patients with and without cystic fibrosis. A NONMEM analysis.

A. Rousseau, F. Saint-Marcoux, J. Debord, P. Marquet.
Department of Pharmacology and Toxicology, University Hospital, Limoges, France.
poster
Background: Cyclosporine (CsA) pharmacokinetics exhibits flat and delayed absorption profiles. Previously a model where the absorption time profile of CsA was described by a Gamma distribution, which convoluted with a two-compartment open model, was implemented in an in-house pharmacokinetic software.
Objectives: development of a population pharmacokinetic (PK) model in lung transplant patients, in order to study the influence of cystic fibrosis on interpatient variability in systemic exposure. 
Patients and methods: a PK population model was developed using concentration-time data from 65 patients receiving oral cyclosporine either twice or three times daily, using NONMEM 5 under Visual-NM. Twenty seven patients had cystic fibrosis (CF) and 38 had not. Post-transplantation delay was 2 weeks to 5 years (15 patients were grafted for less than 3 months). 539 blood concentrations were available (5 to 12 for each patient). The absorption phase was modelled using a subset of gamma distribution simulated using n sequential compartments. This multistage modelling process is characterized by two parameters: the number of compartments (n) and the transfer rate constant. The classical first-order absorption model is a special case of this model since it is obtained when n=1. CsA was assayed by EMIT assay.
The influence of the following individual covariates was studied: age, weight, height, BSA, serum creatinine, and cystic-fibrosis (CF=1 if patient had cystic-fibrosis, otherwise CF=0). In a second approach, the medical status (CF/non-CF) was replaced by different bioavailability factors in the two groups of patients : after attributing a mean arbitrary bioavailability factor F equal to 1 to the non-CF patient group, F' the bioavailability in CF patients and the variability of F and F' were estimated. 
Results: A pharmacokinetic model which combined an absorption phase simulated by 6 sequential compartments and a two-compartment open model better described the data than those using classical zero or first order absorption, even with one lag compartment. Interindividual variability was described by an exponential error model. For all the CsA profiles studied, the mean absorption time (MAT), apparent clearance (Cl/F) and apparent volume of the central compartment (Vc) were 0.71 h, 32.7 L/h and 85.4L respectively (inter-individual variability CV » 25.7; 27.7; 57.4 %). A good estimation of all the population PK parameters was obtained (standard error of estimates/mean 1.7, 4.5 and 8.6% for MAT, CL/F and Vc respectively). The mean Bayesian apparent clearance was significantly higher in patients with CF (p<0.01; 36.0 ± 8.2 versus 30.1 ± 7.7 L/h). This result is consistent with the well-known reduced bioavailabity in cystic fibrosis patients. Of the individual covariates tested, only CF led to a significant decrease of the Objective Function ( i.e. 40 points). Both CL/F and Vc/F were significantly (p<0.001) dependent on cystic fibrosis. Introduction of CF as a covariate on CL/F and Vc/F simultaneously was not redundant. However, the inter-individual variability obtained with the final model was not significantly reduced with respect to the model without covariates (CL/F 28 vs 25% and Vc/F 57 vs 52%). Residual variability consisted of a combined additional (10.2 µg/L) and proportional error (13.6%). 
When taking into account the drug bioavailability instead of the medical status, it was found that F'/F = 0.73, meaning that CsA bioavailability in CF patients was on average 73% that of non-CF patients. Moreover, F and F' showed a variability of 24% and decreased the Objective Function by 50 points.
Conclusion: A population PK model was successfully applied in patients with and without cystic fibrosis that could be useful to improve CsA dose adjustment in this context. No of the following covariates: weight, height, BSA, serum creatinine exhibited any clinically influence on the pharmacokinetics parameters of CsA.

Comparison of alternative models for the analysis of drug disposition profiles showing enterohepatic circulation using a population approach

Gianluca Nucci and Roberto Gomeni
GlaxoSmithKline - Clinical Pharmacokinetics/Modelling and Simulation
poster
Background & Objective: Enterohepatic recycling (ER) is associated with multiple peaks in concentration-time profile. Therefore a model analysis is always needed to assess the pharmacokinetics (PK), and in particular T1/2 and AUCinf of ER drugs. Recently Funaki [1] and Ezzet et al [2] used a population analysis approach for describing the PK of ER drugs. However in these works the timing and number of times the gallbladder emptied were either arbitrarily fixed or limited to one. To overcome these limitations Wajima et. al [3] proposed a new model exploiting periodic transfer rates that accounted for multiple peaks in the plasma profile. Therefore the goal of this study was to apply and optimize the periodic transfer function approach in a population PK study and to assess the impact of different modulating functions. 
Methods: 25 subjects dosed with 0.3 - 6 mg single oral administration of an antidepressant drug contributed to the 321 data samples analyzed. The last sample times ranged from 3 - 191 h post dose. These data, exhibiting ER profiles, were described with a three compartment model (central, peripheral and a bile) with first order absorption and lag time. The bile compartment controls the ER since its transfer rate to plasma is modulated by a periodic function. We tested different periodic functions and several modulating frequencies (either fixed or estimated) and compared them in terms of log likelihood and goodness of fit. 
Results: The best model, based on the modulating function ABS(sin(2*pi* (t+phi)/w)), provided adequate fit to the pooled data. A large intra-patient variability was observed for the estimated amount returning from the bile to the central compartment while the feeding frequency and the delay (from dosing time) for starting the ER process were fairly constant. 
Conclusion: The model developed in this study is suitable for the analysis of population PK of ER drugs. It accounts for multiple peaks, can be applied to multiple dosing without increasing the number of parameters or fixing the feeding time estimation and enables to estimate the optimal recycling frequency. 
References:
1- Funaki T. J Pharm Pharmacol 51, 1999. 
2- Ezzet F. et al. Clin. Ther. 23,2001 
3- Wajima et al. JPP 54, 2002

Markedly different predictions about insulin PharmacoDynamic (PD) measurement feasibility in healthy subjects from recently proposed IntraVenousGlucoseToleranceTest (IVGTT)-based insulin-glucose models

Andreas Groth & Mikael Thomsen
Technical University of Denmark & Novo Nordisk A/S
poster
Objectives: Evaluating the correspondence between insulin PD measurements by glucose clamps and IVGTT-based insulin-glucose models.
Methods: We compared two recent IVGTT-based models: Hovorka et al., AJPEndo 282(5) (M1) vs. DeGaetano/Arino, JMathBiol 40 (M2) with respect to predictions about insulin PD measurement feasibility.
Results: By model structure, M1 predicts that insulin PD effects may be measured with acceptable accuracy by maintaining a realistic control of glucose levels in glucose clamps. M2 predicts that parameter values for each subject determine whether sensitivity to insulin is sufficiently high compared to glucose sensitivity. Assuming 300 pM insulin, the table shows for each M1 subject the relevant reported parameter values followed by our results: The predicted signal-to-noise ratio when measuring insulin PD (+/- 5% glucose is a realistic "noise" level in a glucose clamp). If a 100% difference in insulin level is predicted to elicit less effect on the measured PD than 5% noise on the glucose level, we deem insulin PD measurement predicted non-feasible in that subject. 
Conclusion: Two recently proposed models of insulin action and glucose metabolism in healthy subjects during IVGTT provide very different predictions about achievable accuracy of insulin PD measurements: With the reported parameter values, M2 predicts that accidental small differences in experimental glucose levels may obscure insulin PD measurements in 70% of the subjects studied vs. 0% for M1. 

Subject	Glucose effectiveness
b1
min-1	Insulin sensitivity
b4
pM-1 min-1	Assumed insulin level
pM	% increase in insulin level (signal) required to elicit same effect on glucose disposal as 5% increase in glucose level (noise)	Insulin PD measurement realistically feasible in subject?	
1	0.0226	3.80E-08	300	9917	No	
2	0.0509	1.29E-07	300	6581	No	
3	0.0309	6.99E-07	300	742	No	
4	0.0084	7.55E-05	300	6.9	Yes	
5	0.0273	1.10E-07	300	4141	No	
6	0.0002	1.09E-04	300	5.0	Yes	
7	0.0001	3.73E-04	300	5.0	Yes	
8	0.0565	5.70E-06	300	170	No	
9	0.0135	3.51E-08	300	6415	No	
10	0.0159	8.72E-08	300	3044	No	

A hidden markov model for characterizing the anti-migraine action of triptans

Hugo Maas, Oscar Della Pasqua, Meindert Danhof
LACDR, Leiden University, Division of Pharmacology
poster
Triptans (such as sumatriptan and naratriptan) are efficacious and specific medications in the treatment of migraine. Yet, assessing clear pharmacokinetic-pharmacodynamic (PK-PD) relations for these drugs is difficult. In most clinical studies the actions of triptans in the trigeminal system are measured indirectly using pain-rating scales. As a consequence , sources of variability stemming from the multiple levels of pain control are added to the original trigeminal signal. Furthermore, little is known about the kinetics of pathophysiological mechanisms involved in migraine, which complicates the design of predictive mechanism-based models.
In principle a PK-PD model for triptans should be based on a set of physiologically meaningful parameters. The facts that little information on the disease is available and that the endpoint is a categorical variable, impose that the model be stochastic. A class of structural models that provide these features are the hidden Markov models1.
To test the hidden Markov model concept, a model was developed to describe the course of a single migraine attack. It consists of two layers: i) a hidden layer representing the (unobserved) states of trigeminal activity and ii) an observational layer that transforms trigeminal activity into a headache score. The connectivity between the unobserved states was assumed to be unidirectional, in order of decreasing trigeminal activity. The parameters in this part of the model include the elements of the intensity matrix, which can be considered rate constants of the trigeminal activation process. The headache scores returned by the observational layer are multinomially distributed conditional on the unobserved state. The parameters in this layer are the elements of the emission matrix, reflecting the influence of pain control processes on the trigeminal pain signal. The model was applied to estimate parameters from pain score data obtained from clinical trials with sumatriptan. 
In this analysis the transitions in the hidden layer are functions of plasma drug concentration. Demographic variables such as age and sex were incorporated into both layers to explain variability in pain response. 
1L. Rabiner. A tutorial on hidden Markov models. Proc. IEEE, 77:257--286, 1989.

Population pharmacokinetic analysis of indinavir in HIV-patients treated with a stable antiretroviral therapy

K. Brendel(1), M. Legrand(2), A.M. Taburet(3), G. Baron(1), C. Goujard(4), F. Mentré(1) and the Cophar-1 study group.
(1) INSERM E0357, Department of Epidemiology, Biostatistics and Clinical research, AP-HP, Bichat University Hospital 
(2) Clinical Pharmacology Department, AP-HP, Pitié-Salpétrière University Hospital
(3)Clinical Pharmacy, AP-HP, Bicêtre University Hospital
(4)Internal Medicine, AP-HP, Bicêtre University Hospital
poster
Objectives: The objectives of this study were to build a population pharmacokinetic model that describes plasma concentrations of indinavir in HIV-infected patients with sustained virological response under a stable antiretroviral combination, and to determine inter and intra-individual variability[1]. 
Methods: Data were obtained from 45 patients who received different doses of indinavir; among them, 14 received ritonavir booster[2]. Patients were required to have a baseline plasma HIV RNA 
Results: The population analysis was performed with the First Order method by using WinNonMix. A one compartiment model with first order absorption and first order elimination best described the data. For patients treated with indinavir alone, absorption rate constant was 0.43 h-1, and oral clearance (Cl/F) was 33 L/h; they were 0.25 h-1and 19 L/h respectively for patients treated with indinavir plus ritonavir. Cl/F was found to increase by 1.45 fold in men and by 1.18 fold in patients with zidovudine. Oral volume of distribution (V/F) was 24 L. The inter-individual and intra-individual variability were 117 % and 205 % for V/F, 42 % and 58 % for Cl/F respectively. With simulations, the median, the 10 and 90 percentiles were the highest for women who did not take AZT and the lowest for men who took AZT, both with and without ritonavir. 
Conclusions: 
In this population analysis, we showed the effect of ritonavir on the absorption rate constant and on the clearance of indinavir. We also quantified a large inter and intra-individual variability. A population model including inter-occasion variability had never been implemented in WinNonMix before this study. 
References:
[1] Karlsson MO, Sheiner LB. The importance of modeling interoccasion variability in population pharmacokinetic analyses. J Pharmacokinet Biopharm 1993;21(6):735-50.
[2] Hsu A, Granneman GR, Cao G, Carothers L, Japour A, Shourbagy T. Pharmacokinetic interaction between ritonavir and indinavir in healthy volunteers. Antimicrob Agents Chemother 1998;42(11) :2784-91.

Population pharmacokinetic modelling of Emfilermin in healthy postmenopausal women and in women undergoing Embryo Tranfer (ET)

Nguyen T. X. Q.(1), Munafo A. (1), Goggin T. (1)
(1) Serono International S.A, Geneva, Switzerland
poster
Background: Current evidence suggests that endogenous leukaemia inhibitory factor (LIF) - a heavily glycosylated cytokine plays a physiological role in embryo implantation (1,2). Clinical trials with recombinant human leukaemia inhibitory factor (r-hLIF - obtained in E. coli and consequently non glycosylated) are in progress to assess its potential therapeutic role in overcoming embryo implantation failure following IVF (In Vitro Fertilisation) and ET.
Purpose: The purpose of this analysis was to describe the pharmacokinetics of recombinant-hLIF (Emfilermin; AMRAD Corp. Ltd, Australia) in healthy postmenopausal women and in women with recurrent implantation failure (RIF) who undergo IVF and ET.
Methods: Data from the following studies were combined. 
Study 1 :  was a double-blind, randomised, placebo-controlled, phase I study in twelve healthy oestrogenised postmenopausal women (mean age: 57 ± 5 years). Subjects received 150 µg of Emfilermin or placebo SC twice daily during 7 days. Frequent pharmacokinetic sampling was performed on day 1 and 7.
Study 2 : was a double-blind, randomised, placebo-controlled, proof of concept study in sixty-six young women with RIF justifying IVF and ET (mean age: 33 ± 2 years). Patients received 150 µg of Emfilermin or placebo SC just before ET and twice daily for 7 days. Pharmacokinetic sampling was sparse and was done on Days 1, 4 and 7.
Non-compartmental analysis on serum LIF concentrations was performed using WinNonLin version 4.0. Population pharmacokinetic analysis was performed using NONMEM version V.  
Results: Non-compartmental analysis of data of Study 1 showed an apparent terminal half-life at 2.5 h (median value), which was similar on day 1 and day 7. An accumulation ratio of 1.3-1.5 was observed in 4 out of 10 subjects, unexplained by the observed half-life. The reason for this could not be determined. 
The subsequent population pharmacokinetic analysis was performed on (assumed) steady-state data only (day 4 and day 7). A one-compartment 
disposition model with zero order input was used. The duration of the absorption was 1.1 h. Inter-subject variability on this parameter was negligible. The apparent volume of distribution was 184 L (with a CV of 28%)and devoid of any significant covariate effects. The observed CL/F on Study Day 7 was 31% higher compared to the Study Day 4 (Study Day modelled as a covariate). In addition the systemic clearance in younger women with RIF was reduced by 40% compared to that in older healthy women (which was 61.3 L/h with a CV of 11%). CL/F was also found to be roughly proportional to body weight, with a 2?fold increase in body weight resulting in a 1.9-fold increase in CL/F.
The geometric mean post-hoc estimates of apparent clearance and volume of distribution and their variability were consistent with the population estimates. In healthy subjects, results were fully consistent with those obtained using non-compartmental methods. The residual variability on r-hLIF serum levels was quite low (CV = 17%).

Conclusion: Recombinant -hLIF pharmacokinetics are quite complex. The initial assumption of steady-state is not supported by the results of this analysis, which suggests possible time dependence in the apparent clearance of r-hLIF,higher on Day 7 compared to Day 4. All available pharmacokinetic data will now be combined and analyzed to further characterize this possible phenomenon. The clinical impact of this non-stationarity is however mitigated by the fact that the observation period in this experiment corresponds to the intended duration of treatment (7 days)
in this indication.

References:
1- Laird, S.M., Tuckerman, E.M., Dalton, C.F., Dunphy, B.C., Li, T.C. and Zhang, X. (1997)  The production of human leukemia inhibitory factor by human endometrium: presence in uterine flushings and production by cells in culture.  Human Reproduction 12, 569-574.
2- Hambartsoumian, E. (1998)  Endometrial leukemia inhibitory factor (LIF) as a possible cause of unexplained infertility and multiple failures of implantation.  American Journal of Reproductive Immunology 39, 137-143.

Evaluation by simulation of tests based on non-linear mixed-effects models in interaction and bioequivalence cross-over trials

Xavière Panhard, France Mentré
INSERM E0357, Department of Epidemiology, Biostatistics and Clinical Research,
University Hospital Bichat – Claude Bernard, Paris, France.
poster
Objectives : Evaluation of tests based on non linear mixed- effects models (NLMEM) in pharmacokinetic interaction and bioequivalence cross- over trials comparing a test and a reference treatment (or formulation). Comparison to standard tests recommended by FDA [1] and EMEA [2,3], based on non compartimental (NC) AUC.
Methods : We proposed 4 tests based on NLMEM for AUC comparisons in interaction cross-over trials: a likelihood-ratio test (LRT), a Wald test and two tests, parametric and non parametric, comparing the individual Empirical Bayes (EB) estimates. These tests were adapted to the case of equivalence, except the LRT which does not have any simple extension. For both interaction and equivalence studies, we evaluate by simulation the type I error a (5000 simulated studies) and the power (1000 simulated studies for each alternative hypothesis) of these tests. Data for a usual PK model were simulated using Splus software and analysed with its function nlme [4]. As the estimation of a is expected to be different from its nominal value, we use a correction of the significance threshold for the evaluation of the power of interaction tests. That correction is not performed on bioequivalence tests, for which the null hypothesis is composite. Different configurations of the number of subjects N (12, 24 and 40 ) and of the number of samples per subjects n (3, 5 and 10) were studied.
Results : In the original configuration (N=12, n=10), the two global test (LRT and Wald) have a type I error a far superior to 5%, decreasing when N increases. When N is fixed, a increases with n. Power is satisfactory for both tests, after correction of the significance thresholds. Results of EB and NC tests are similar with satisfactory powers and a type I error rate close to 5%, except when n=3 for EB tests (that particular number of samples does not allow for the calculation of the NC AUC). Similar results were obtained for equivalence tests.
Conclusion : NLMEM can be useful for early phases cross- over studies. The evaluation by simulation of the properties of the tests is however necessary because of the inflation of the type I error. These methods were evaluated in the ANRS 110 trial, which studies the absence of PK interaction between nelfinavir, a protease inhibitor, and a cholesterol lowering drug.
References :
[1] FDA. Guidance for industry - population pharmacokinetic, 1999.
[2] EMEA. Note for guidance on the investigation of bioavaibility and bioequivalence, 2000.
[3] EMEA. Note for guidance on the investigation of drug interaction, 1998.
[4] Pinheiro JC and Bates DM. Mixed-effect models in S and Splus. Springer- Verlag, New York, 2000.

Population pharmacodynamic analysis of dabigatran, the active form of the new oral direct thrombin inhibitor dabigatran etexilate (BIBR 1048), on the prolongation of aPTT and ECT in orthopaedic patients.

K.H. Liesenfeld, C. Tillmann, I. Troconiz (#), H.G. Schaefer, J. Stangier
Boehringer Ingelheim Pharma GmbH & Co. KG, (#) School of Pharmacy, University of Navarra, Pamplona, Spain
poster
Introduction: The oral direct thrombin inhibitor prodrug dabigatran etexilate is under development for the prevention of deep vein thrombosis in patients at risk of thrombotic events. The effects of the active principle dabigatran (BIBR 953 ZW) on the activated partial thromboplastin time (aPTT) and ecarin clotting time (ECT) were assessed in a dose escalation safety study (BISTRO I) involving 289 patients treated with 12.5 to 300 mg dabigatran etexilate B.I.D. and 150 and 300 mg Q.D. for 6 - 10 days. 
Methods: Dabigatran plasma concentrations and the pharmacodynamic parameters aPTT and ECT were measured 4 hours after the first dose, before drug administrations (trough), 2 h post dose, and by frequent sampling at steady state. In total, 287 patients were included in the population analysis of aPTT and ECT. 
Results: Pharmacodynamic model for aPTT: The relationship of dabigatran plasma concentrations and aPTT was best described by combining an Emax model with a linear model as shown by the following equation: aPTT = BASE + (EMAX*CONC /(EC50+CONC)) + SLOP*CONC Interindividual variability (IIV) was allowed on EMAX, BASE, SLOP and EC50. The typical (population) values of EMAX and BASE itself were a function of time after surgery: EMAX = EMA0 * (1 – (EMMX * TIME/24) / (ET50 + TIME/24)) BASE = BAS0 * (1 – (EMBA * TIME/24) / (ET50 + TIME/24)) The typical estimate of the initial baseline aPTT (BASE, time=0) was 33.4s. The typical values for EMAX (initial) and EC50 were 26.9 s and 94.7 ng/mL, respectively. SLOP, which gives the typical slope of the linear relationship between CONC and aPTT, was 0.0509 s/(ng/mL). This decline in the typical values of EMAX and BASE was modelled by an inhibitory EMAX-model. The half-life (ET50) of the decline was approximately 1.6 days for both EMAX and BASE and the maximum decline about 46.3% for EMAX and 10.2% for BASE, respectively. Pharmacodynamic model for ECT: The relationship of dabigatran plasma concentrations and ECT was described by a linear function: ECT= BASE + SLOP * CONC Interindividual variability was allowed on SLOP (14%) and BASE (8%). The typical (population) values for BASE and SLOP itself were a function of time after surgery. The typical value of the initial baseline ECT was 28 s (BASE, time=0). The decrease in BASE was described by an inhibitory EMAX model (similar to aPTT) with a half-life of baseline decline of 2.9 days and a maximum decline of 17.5%. The typical value of the slope of the plasma concentration-ECT relationship (SLOP) decreased from initially 0.38 s/(ng/mL) to 0.27 s/(ng/mL). The decrease in SLOP was described by a combination of two exponential terms: SLOP = SLO0*EXP(-KM*TIME)+SLOFinal*(1-EXP(-KM*TIME)) The residual variabilities of aPTT and ECT were 7.6 and 6.6%, respectively. The covariate analysis (patient demographics, treatment variables and co- medications) indicated that the model parameters were not affected by any of the tested covariates. 
Conclusions: The population pharmacodynamic investigation of the effect of the direct thrombin inhibitor dabigatran revealed a close correlation between drug plasma concentrations and effect on blood coagulation. The relationship between dabigatran plasma concentrations and ECT was linear, whereas the plasma concentration - aPTT relationship was best described by a combined Emax and linear model. The time-dependency in the aPTT- as well as the ECT-model indicates, that for a given dabigatran concentration the observed increase in aPTT and ECT would be larger early after surgery and less at later times. This observation can be rationalised by peri/post surgical effects on hemostasis, e.g. volumes of transfusion administered during surgery. 

Probabilistic Risk Assessment Using Integrated Preclinical-Clinical PK/PD Modelling in NONMEM

Philip J. Lowe (1) and William Sallas (2)
(1) Modelling and Simulation Section, Preclinical Safety, Novartis Pharmaceuticals AG, 4002 Basel, Switzerland; (2) Clinical Modelling and Related Technologies, Clinical Development and Medical Affairs, Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, USA.
poster
Objective: To assess the clinical risk of an adverse effect seen only in preclinical safety studies.
Methods: PK + PD data were obtained from toxicology studies (N=90) and PK from clinical Phase II and III studies (N=1543). For the PD, after checking that time delay hysteresis was not occurring, a sigmoid Emax function was used for the concentration-effect model. The clinical population PK utilised a one compartment system with first order absorption. For the risk assessment simulations, the clinical PK model for steady-state Cmax drove the preclinical PD model, with a team-agreed assumption of equal species sensitivity to the drug. Monte-Carlo simulations were carried out from a clinical population demographic database of 1117 patients who matched the dosing criteria. Subproblems=200 gave 223400 observations from which to count events of clinical concern. Uncertainty in the PK, PD and variance parameters was assessed by repeating the simulation 30 times with random parameter values drawn from distributions of those parameter values.
Results: In the clinical PK model, many covariates were found for patient demographic features. Only two of these were large enough to warrant changes in dose and regimen. Bodyweight and baseline disease status were used in the creation of a dosing table. The toxicology PD model was characterised by individual parameters for baseline, IC50 and Hill coefficient for each animal. Of 223400 simulated patients, none gave a clinically significant response, therefore the mean risk was judged to be less than 1 in 223400. After parameter uncertainty was taken into account the 95% prediction interval for the risk was estimated to be from 1/17000 to <<1/223400.
Conclusions: A scheme for assessing the probability of a toxicologically observed adverse effect being a risk to human health is presented, using an extension to the population PK modelling commonly carried out in drug development. The process relies on a number of assumptions which are either supported by data, or purposely set to be conservative. For drugs more complex than the case presented here, extra features could and should be built into the model to account for interspecies differences.

Computer-Assisted Trial Design (CATD) for PEG-IFN with Using PD Marker to Predict Efficacy

T. Funaki(1), Y. Gao(2), R. Wada(2), K. Nakai(1), K. Miura(1), H. Kinoshita(1)
(1)Chugai Pharmaceutical Co. Ltd., 1-9, Kyobashi 2-Chome, Chuo-ku, Tokyo, 104-8301 Japan; (2)Pharsight Corporation, 800 W. El Camino Real, Suite 200, Mountain View, California 94040, U.S.A.
poster
Computer-assisted trial design (CATD) approach in drug development has recently been increasing to assure qualitative and efficient conduct of clinical trails. Pegylated interferon α-2a (PEG-IFN) is interferon α-2a in which one branched polyethylene glycol molecule with an average molecular weight of 40K daltons is conjugated. The half-life of pegylation increases, thereby providing greater exposure and efficacy and allowing to be once a week administration. In this study, CATD model for PEG-IFN was established to investigate the relationship between 2', 5'-oligoadenylate synthetase (2',5'-OAS) activity as PD marker and efficacy of PEG-IFN, where once a week administration was assumed to be done for 48 weeks and assumed to be evaluated efficacy (virological and biochemical responses) at weeks 48 and 72. 
The population PK/PD model established in a healthy volunteer study was used to establish the CATD model, where an indirect response model (stimulation - kin) was used to describe PD of PEG-IFN. The literature data of virologic responses, biochemical responses and dropout rates were used to predict the possible range of clinical responses. The simulated 2',5'-OAS activity at week 48 was used to link PK/PD to clinical response since observed 2',5'-OAS activity at week 48 was not available in healthy subjects.
The current CATD model well describes the virological and biochemical responses at weeks 48 and 72, where a single Emax model was used to describe the relationship between efficacy and PD marker/dose. These results confirm the value of applying the CATD approach to support the clinical development of PEG-IFN as well as other potential products. 

Bayesian Estimation of Epirubicin Clearance by Limited Sampling

Lorraine D. Ralph1,2, Alison H. Thomson1,3, Nicola A. Dobbs4, Chris Twelves5
1Div of Cardiovascular & Medical Sciences, University of Glasgow, UK, 2Quintiles Ltd, Heriot-Watt University Science Park, Riccarton, Edinburgh, UK, 3Pharmacy Dept, Western Infirmary, Glasgow, UK. 4Cancer Research UK, London, UK. 5Cancer Research UK, Dept of Medical Oncology, University of Glasgow, UK.
poster
Introduction: Epirubicin is a cytotoxic anthracycline that is active against a wide range of tumours, including early or advanced breast cancer. A limited sampling approach to estimate the pharmacokinetics of epirubicin could be useful to aid the design of future studies or for use in adaptive feedback control and dosage individualisation. 
Methods: The data set comprised 105 patients with advanced or metastatic breast cancer treated with single-agent epirubicin. Epirubicin was administered as a slow bolus injection and a mean of 12 blood samples per patient were collected. The pharmacokinetics of epirubicin were described using a 3-compartment model with proportional residual error. Optimal sampling times were identified by D-optimality using ADAPTII and used to propose 10 limited sampling designs. The data set was truncated to include the sampling times for each of the designs and Bayesian estimates of CL were obtained using NONMEM. CL estimates from each limited sampling design were compared to CL estimates obtained using all the data. A data set of 200 patients was simulated to assess the sensitivity of the best limited sampling designs to errors of up to 20 % in the recording of sample times. 
Results: The optimum sampling times were: end of the infusion and 18 min, 40 min, 3 h, 10 h and 48 h post-start of the infusion. The best 3-sample design included samples at 40 min, 3 h and 48 h and gave estimates of CL that were unbiased and had an imprecision of 9.1 %. The best 2-sample design included samples at 3 and 48 h and produced unbiased estimates of CL with an imprecision of 12.4 %. Poor estimates of CL were obtained if a 48 h or 24 h sample was not included. Simulations that included errors of up to 20 % in the recording of the blood sampling times had negligible effects on the bias and imprecision of CL estimates. 
Conclusion: Limited sampling designs have been identified that can estimate epirubicin CL with adequate precision and bias from 2 or 3 blood samples. These designs were flexible for blood sample collection times and are robust with regard to sample time recording errors.

Power, Selection Bias And Predictive Performance Of The Population Pharmacokinetic Covariate Model

Jakob Ribbing and Niclas Jonsson
Uppsala University
poster
Identification and quantification of covariate relationships is an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modeling. The covariate model is often built in a stepwise manner. With such methods, selection bias may be a problem, if the covariate model is selected based on the same data as used for estimating the model parameters. Competition between multiple covariates could further increase selection bias [1], especially when there is a high correlation between the covariates, and could result in a loss of power to find the true covariates.
The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and some states of nature (se below).
Data sets with 20 to 1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation (r=0, 0.15, 0.50 and 0.85, respectively) to the other four covariates. Data sets, in which each individual had 2 or 3 PK observations, were simulated using a one compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter individual variability in the structural model parameters was also introduced to the simulation model. 7,400 replications were simulated independently, for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified p-value) the different covariates, along with the estimated covariate coefficient was recorded.
The results show that selection bias is very high for small datasets (50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to twice its true value, rendering the covariate model useless for predictive purposes. Surprisingly, all though competition from false covariates caused substantial loss in the power of selecting the true covariate, selection bias increased only marginally if statistical significance was required. Without the competition, there was a clear link from the power of selecting a true covariate to bias and predictive performance of the selected covariate model.
Reference: 
[1] Miller, A. J. (1984). "Selection of Subsets of Regression Variables." Journal of the Royal Statistical Society. Series A (General) 147(3): 389-425. 

Population Pharmacokinetics of Amphotericin B Lipid Complex in Neonates

Gudrun Würthwein (1), Georg Hempel (2), Felice C. Adler-Shohet (3), Jay M. Lieberman (3), Thomas J. Walsh (4), and Andreas H. Groll (2)
(1) Coordination Center for Clinical Trials and (2) University Children`s Hospital, - Paediatric Haematology/Oncology -Muenster, FRG; (3) Millers Children's Hospital, Los Angeles, LA, USA; and (4), Immunocompromised Host Section, NCI, Bethesda, MD, USA
poster
Objectives: Amphotericin B Lipid Complex (ABLC) is as effective but better tolerated as conventional amphotericin B. Little is known, however, about its disposition in neonates. We therefore investigated the plasma pharmacokinetics of ABLC in premature neonates with invasive fungal infections and determined covariates accounting for interindividual variability.
Patients and Methods: Sparse plasma data (153 samples; 1 to 9 per patient, sampled at 1 to 254 h after drug administration) of 28 mostly premature neonates (median weight: 1.06 kg; range: 0.48-4.9; median gestational age: 27 weeks; range: 24-41) enrolled in a multicenter phase II study were analyzed. Patients received either 2.5mg/kg (n=15) or 5mg/kg (n=13) once daily over 1 or 2 hours, respectively, for a median duration of 21days (range: 4-47). Concentrations were measured in whole blood and quantified as total amphotericin by a validated HPLC method. Weight (WT), postnatal age (AGE), gestational age (GA), days on drug, sex, dosage group and prior amphotericin B deoxycholate treatment (DAMP) were documented as potential covariates. Data were analyzed using NONMEM version 5 and XPOSE 3.01.
Results: In a first step, data for time after dose (TAD) £ 24h (n=130) were best fitted to a one compartment model with an additive error model for residual variability, WT3/4 as a covariate on clearance (CL) and WT1 as a covariate on volume of distribution (V) (1,2). Potentially significant covariates detected by GAM were DAMP, AGE and GA on CL and DAMP on V. After backward exclusion (p<0.01) none of these covariates significantly decreased the objective function. The final model equations were: CL [l/h] = 0.399xWT3/4 (IIV=35%); V [l] = 10.5xWT (IIV=43%). 
In a second step, a two compartment model was applied in order to model all data (additional n=23 datapoints for TAD 24-245h). However, the number of data was too small to describe the terminal phase sufficiently. Compartment free analysis of collected observed, dose normalized data with TAD>24h showed a terminal elimination half-life of 395h which is in good agreement with results reported for other pediatric age groups and adults (3,4).
Conclusions: This is the first report of ABLC population pharmacokinetics in premature neonates. Weight was the only covariate that significantly influenced the clearance of amphotericin B from blood. 
1.	Holford NHG, Clin Pharmacokinet 1996, 30, 129-32 
2.	West GW et al, Science 1997, 276, 122-6 
3.	Adedoyin A et al, Antimicrob Agents Chemother 2000, 44, 2900-2 
4.	Walsh TJ et al, Antimicrob Agents Chemother 1997, 41, 1944-8

Population pharmacokinetics of cisapride in preterm and term neonates

C. Le Guellec, F. Odoul, A. Henrot, G. Paintaud, E. Saliba, M.-C. Saux, E. Autret-Leca
Department of pharmacology, Tours University Hospital, FRANCE
poster
Background: Cisapride is used in neonates with gastro-oesophageal reflux. Nevertheless, only one pharmacokinetic study has been performed in this population. The aim of our study was to estimate pharmacokinetic parameters of cisapride in preterm and term neonates and their interindividual variability. 
Methods: Neonates were administered cisapride orally 0.2 mg/kg four times a day. QT intervals were measured before and 48h after the first dose. Blood samples were drawn during an other biological control, at various times after dosing. Plasma concentrations of cisapride were measured using a validated HPLC method. Demographic and biological data and co-administered drugs were studied as possible covariates influencing cisapride pharmacokinetics. Data were analysed using NONMEM software with a one-compartment model. 
Results: Ninety one subjects (45 girls and 46 boys), with gestational age: 26 - 37 weeks, birth weight: 750 - 2780 g and height: 32 - 50 cm were included. No side effect has been reported during the study. Plasma cisapride was measured in 250 samples (1 to 7 per subject) obtained from 2 to 123 days of life, between 10 min and 13.5 h after dosing. Cisapride concentrations ranged 5.5 - 172 ng/mL. Since too few samples were drawn early after dosing, the absorption constant was fixed to 2.5 h-1. Mean population clearance was 1.24 L/h and volume of distribution was 16.7 L (interindividual CV = 43.5 % and 17.2 %, respectively). Clearance was significantly related with weight and with both birth weight and postnatal age; interindividual CV of clearance and volume were 38 % and 36 %, respectively. No significant relationship was found between volume of distribution and any covariate. 
Conclusion: As evidenced in our study, cisapride clearance in neonates is influenced by weight and data confirm that current recommendations of dosing on a weight-basis is not associated with unexpectedly high concentrations. 

Population pharmacokinetic analysis of the new oral thrombin inhibitor dabigatran etexilate (BIBR1048) in patients undergoing primary elective total hip replacement surgery.

C.Tillmann, I.F. Trocóniz (#), J. Stangier, K. H. Liesenfeld, H.G. Schaefer
Boehringer Ingelheim Pharma GmbH & Co KG, (#) School of Pharmacy, University of Navarra, Pamplona, Spain
poster
Introduction: Dabigatran etexilate (BIBR 1048) is an orally available double prodrug of the active principle dabigatran (BIBR 953 ZW), which exerts potent anticoagulant and antithrombotic activity. Dabigatran etexilate is currently in phase II clinical development. 
Objectives: Study 1160.11 (BISTRO I) was the first clinical trial with Dabigatran etexilate in the target population (i.e. patients undergoing primary elective total hip replacement). The aim of the analysis was to develop a population pharmacokinetic (PK) model in order to describe the dose- concentration relationship of BIBR 953 ZW and to characterise both, the inter- individual (IIV) and residual variability as well as to quantify the relationship between covariates and PK model parameters. 
Methods: A PK population model was developed using NONMEM (Version 5) on a UNIX (HP UX ver.11.0) platform. A total of 4604 plasma concentrations obtained from 287 patients after once or twice daily oral dosing for up to 10 days after surgery in the dose range 12.5, 25, 50, 100, 150, 200 and 300 mg were available for the analysis. Structural PK models were parameterised in terms of apparent volumes of distribution, clearances for distribution and elimination and absorption rate constants. Twenty-five covariates containing patient demographic factors and treatment variables were tested to evaluate their influence on the pharmacokinetic parameters. 
Results: Pharmacokinetics of dabigatran were best described by a two compartment body model with first order absorption and first order elimination. Inclusion of a lag time was also required. The rate constant of drug absorption (KA ) during the first day of treatment was significantly lower (p<0.01) compared to days 2 to 10. In addition, the data supported the estimation of different degrees of IIV KA and apparent plasma clearance (CL/F) between day 1 and days 2 to 10 after surgery. The following estimates for IIV were obtained: Day 1, 109 % (CL/F), days 2 to 10, 30 % (KA), 46 % (CL/F). Estimates of residual variability differed also between the two occasions (day 1 vs. days 2-10): 67% vs 36%. Age and serum creatinine (SCR) influenced significantly KA (p<0.01), whereas gastrin (GAST), and creatinine clearance (CRCL), only for days 2-10, effected CL/F. The typical values for KA for a 67 years old patient with SCR of 0.964 mg/dL were 0.022 h-1 and 0.093 h-1 on day 1 and days 2 to 10, respectively. The typical value for CL/F on day 1 for a patient with GAST of 34.58 pmol/L was 70.87 L/h, whereas on days 2 to 10 the typical CL/F was 106.2 L/h for a patient with GAST of 34.58 pmol/L and CRCL of 76.16 mL/min. The typical estimates (SE) for the apparent volumes of distribution of the central and peripheral compartments were 30.8 L (17%) and 136 L (42%), respectively. The typical value (SE) of intercompartmental clearance, was 13.6 L/h (36%). Inclusion of the above mentioned covariates resulted in a 12, 4 and 8 % (absolute) reduction in the initial unexplained interindividual variability found in KA and CL/F (day 1, days 2 to 10), respectively. 
Conclusions: These results show that during the first 24 hours after surgery the pharmacokinetics of dabigatran are different compared to the following days. This is most likely due to alterations in gastric motility and gastric pH following surgery. As a consequence, the rate of absorption is reduced and interindividual variability in drug exposure increased. On the following days the PK behaviour of dabigatran is less variable. Several covariates influencing pharmacokinetic parameters were identified. However, their impact on biomarkers for bleeding (aPTT, ECT) will be evaluated integrating pharmacokinetics with pharmacodynamics. 

Pharmacokinetic analysis of paclitaxel administered per os in Swiss mice after a pre-treatment with recombinant interleukin-2 (rIL2).

C. Jamois(1,2,3), E. Comets(3), L. Bonhomme-Faivre(1,2) and F. Mentré(3).
Laboratoire de Pharmacologie, Service Pharmacie, Hôpital Paul Brousse, Assistance Publique des Hôpitaux de Paris (APHP), Villejuif, France (1); Unité Propre de Recherche de l'Enseignement Supérieur 2706, Barrière et passage des médicaments, Faculté de Pharmacie de Chatenay Malabry-Paris XI, France (2); Département d'épidémiologie, biostatistiques et recherche clinique, Hôpital Bichat-Claude-Bernard, APHP, Paris, France (3)
poster
Objectives: Paclitaxel is a potent anticancer drug with proven activity against a broad range of human malignancies, including ovarian and breast cancer and non-small cell lung carcinoma. Its oral bioavailability is low and limits extensive use of oral administration.
Intestinal P-glycoprotein (P-gp) is held responsible of the poor bioavailability in vivo, because it transports paclitaxel towards the extracellular matrix, limiting its absorption from the intestinal lumen. 
Recombinant interleukin-2 is known to induce a decrease in the protein expression of intestinal P-gp and in the level of CYP-450 in vivo in mice, which is directly related to a decrease in intestinal P-gp activity and to a suppression of hepatic drug metabolism. Those two last points can greatly enhance the oral bioavailability of paclitaxel.
To further study on the feasibility of a clinically effective oral formulation of paclitaxel, it was investigated in our present study whether a 3-day pre-treatment with intraperitoneal rIL2 had a pharmacokinetic effect on paclitaxel profile given per os in Swiss mice.
Materials and methods: 96 mice were allocated to two groups receiving either paclitaxel alone (10 mg/kg by oral route) or rIL2 (16.5 µg twice daily from day 1 to day 3) and were given paclitaxel on day 4 (10 mg/kg by oral route).
Plasma concentrations were measured by High Performance Liquid Chromatography after solid-liquid phase extraction. 
Pharmacokinetic profiles were analysed first by the Bailer method, and then using a compartmental approach with software R (freeware equivalent of the statistical language Splus, library nls2).
Results: A complex absorption of paclitaxel has been revealed. The Bailer method showed that the mean AUC values over 0 to 24 hrs were not significantly different in the two groups, but the AUC over 0 to 0.5 hrs were significantly higher in the pre-treated group. 
The compartmental analysis has confirmed these results. In the final model, the fraction of drug absorbed during the first phase, has increased significantly in group pre-treated by rIL2, which might be due to the inhibitory effect of rIL2 on intestinal P-gp, whereas the elimination rate constant (Kel) remained the same across both groups. 
Conclusion: This pharmacokinetic study showed that, a 3 day pre-treatment with rIL2 is able to increase paclitaxel absorption for 15 minutes following an oral input of paclitaxel but elimination is not modified. Recombinant interleukin-2 could enhance its oral bioavailability.

A Markov Model For The Effect Of Covariates Including Drug Adherence On Longitudinal Viral Response In HIV Patients

L. Labbé (1), S.M. Hammer (2), J.W. Mellors (3), S. Rosenkranz (4), L.B. Sheiner (1), and the ACTG 398 study team
(1) Departments of Laboratory Medicine and Biopharmaceutical Sciences, University of California San Francisco, San Francisco, CA; (2) Division of Infectious Diseases, Department of Medicine, Columbia University College of Physicians and Surgeons, New York, NY; (3) Division of Infectious Diseases, Department of Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA; (4) Statistical and Data Analysis Center, Harvard School of Public Health, Boston, MA
poster
Objectives: We investigate the effect of adherence to prescribed antiviral drugs on viral response in PI treatment failures randomized to additional medications in clinical trial ACTG 398 using a Markov model, based on that proposed by Vrijens [1], of the bi-monthly viral RNA increment/decrement. The analysis illustrates the use of multiple imputation and bootstrap with a mixed-effects model.
Methods: All bi-monthly viral RNA values within each patient are categorized into one of three classes: low (L: log10RNA ≤ 2.5) / med (M: 2.5 < log10RNA ≤ 4) / high (H: log10RNA > 4). The response (Y) for each inter-observation interval is the change in RNA category over the interval (decreases (D)/remains the same (S)/increases (I)). Covariates (X) are pre-study exposure to NNRTI (N; a baseline variable), duration of 398 therapy (T; early/late), and drug adherence (ADH; see below) during the interval, as measured by questionnaire (AQ) and electronic compliance monitoring caps (MEMS). Different summaries of daily MEMS-based exposure were evaluated: moments of the distribution of inter-dose intervals, as used by Vrijens [1], fraction of inter-dose intervals greater than a specific value, and fraction of days on which medication was taken. All independent variables were dichotomized by finding the cut-point yielding highest explanatory power in the model. The Markov property is conferred by conditioning on starting RNA value (RNASTART). Due to the fact that probabilities must add to unity and certain transitions (e.g, Y=D| RNASTART=L) are impossible, the 3 responses × 3 values of RNASTART = 9 possible transition probabilities at any setting of X can be uniquely specified using only 4 parameters (A1-A4), modeled as 
ln(Ai) = bij*Zij + bij*Zij*T + bij*Zij*N + bij*T*N + hi, 
i,j=1,4, where, Zij = 1 + aij*ADH, ADH = l*MEMS + (1-l)*AQ, the b, a, and l are parameters to be estimated, and the hi are normally distributed random individual effects. NONMEM is used for estimation, which is stabilized by penalizing all fixed-effect parameters, except for the baseline effect (b11), for deviation from zero, the "null" value. Multiple imputation is performed for missing MEMS and AQ. Standard-errors are estimated by bootstrap. 
Results: New treatment duration (T) and prior exposure to NNRTI are significant: the objective function (OF) decreases by 86. The best cut-off point for T (early vs. late) is 2 months. ADH = average (l = 0.537) of MEMS and AQ significantly affects RNA (OF decrease = 11.5). For MEMS, the simple fraction of compliant days is as good as any other measure tested. 
Conclusion: We have defined a Markov model for the direction of viral RNA change at bi-monthly intervals in extensively treated AIDS patients. The model recognizes the influences of prior RNA (Markov property), drug adherence, time since start of (new) treatment, and prior exposure to NNRTIs. 
References:
[1] Vrijens B. Analyzing time-varying patterns of human exposure to xenobiotics and their biomedical impact. PhD Thesis. University of Ghent, 2002. Ghent, Belgium. 

Population approaches for quantitative PET imaging

A. Bertoldo, G. Sparacino, C. Cobelli
Department of Information Engineering, University of Padova, Italy
poster
Objectives: Quantification of PET images requires the adoption of a model to measure physiological parameters. Usually, parameter estimation is performed, in any given region of interest (ROI), by least squares (LS). Often, however, the signal-to-noise ratio (SNR) of PET data is, relative to model complexity, too low to allow reliable LS estimation. The goal here is to study the feasibility of a "ROI" population approach in PET.
Material & Methods: PET imaging of femoral skeletal muscle with [18F]FDG was performed in 4 healthy male volunteers. Arterial blood samples were also collected along all the experimental time. Eight ROIs were drawn on the [18F]FDG images of each subject in the anteromedial muscle compartments of the femoral region, carefully avoiding the great vessels. The four-compartment five-rate-constant (5K) model developed for describing [18F]FDG kinetics in human skeletal muscle was used for image quantification. For each subject, parameter estimates of 5K model were obtained in each ROI both by LS and by nonlinear mixed-effects modeling with a ROI population described by the 8 drawn ROIs. The Iterative Two Stage method was also considered as a possible computationally attractive alternative to nonlinear mixed-effects modeling. The mixed-effects modeling was performed using NONMEM. The ITS algorithm was implemented in Matlab6. 
Results: By using LS, positive parameter estimates and "reasonable" CV (i.e. <500%) were obtained in 6 of the 8 ROIs for the first two subjects and only in 1 and 4 of the original 8 ROIs in the remaining two subjects. By using NONMEM-FOCE, successful convergence of parameter estimation was achieved in all ROIs. NONMEM-FOCE allows the calculation of individual estimates with precision comparable or better than that obtained using LS also when LS parameter precision is unacceptable. It is of note that NONMEM-FOCE estimated fixed-effects describe an interROI variability very different from that obtainable using the simple mean and variance of LS estimates. With respect to LS and mixed-effects modeling results, ITS allows the calculation of more precise individual estimates for all the ROIs in all the subjects. ITS algorithm convergence was achieved after few iterations. We did not detect any significant difference (P<0.05) between individual NONMEM and ITS estimates.
Conclusion: The results show that the use of population approaches allow a more accurate and more precise determination of parameters of kinetic models from PET data, even in the presence of highly noisy images. In particular, ITS has the potential to allow a reliable and computationally less intensive than NONMEM quantification of the images.

Population PK/PD Modeling of Testosterone (T), LH and Dihydrotestosterone (DHT) Response to Single SC Degarelix in Male Volunteers

Ulrika S.H. Simonsson, Thomas Senderovitz and Mats O. Karlsson
Uppsala University, Sweden and Ferring Pharmaceutical A/S, Denmark
poster
The aim was to describe the response to degarelix, a GnRH antagonist for prostate cancer using nonlinear mixed effects modeling of data from 60 subjects. Degarelix showed flip-flop PK with a long terminal half-life (47 days). A mechanism-based model for the degarelix/LH/T interaction included competitive antagonism of degarelix (estimated Ki= 0.0642 ng/ml) with an endogenous agonist (EA) for GnRH receptors. Production rate of LH was linked to the fraction activated receptors through a spare receptor model (R50=0.20, baseline [EA]/[EA]50= 0.39). A continuous suppression of LH/T led to receptor down-regulation, in the model estimated to a 93% decrease of receptor density at full suppression of T and a receptor mean residence time (MRT) of 4.5 days. A turn-over model described the conversion of T to DHT with a MRT of 6.2 hours. Through a mechanism-based model, the complex interplay could be described and potentially used for prediction.

Population Whole Body Physiologically based Pharmacokinetic/Pharmacodynamic modelling in drug development: Impact of input parameters variability and incertainty on pharmacodynamic response

Sabrina Salhi and Roberto Gomeni
GlaxoSmithKline - Clinical Pharmacokinetic & Modelling and Simulation, Verona, Italy
poster
Objectives:A Physiologically Based Whole Body Pharmacokinetic/ Pharmacodynamic (WBPBPK/PD) is today recognised as knowledge- based mechanistic modelling approach to integrate the current information on a compound across species. This approach constitutes a rational basis to scale-up in-vitro and preclinical data to human, to explain differences among compounds based on physicochemical and structural properties and to predict likely PK/PD response in humans. The aim of this study was to develop and validate a population WBPBPK/PD model for CNS compounds considering the impact on predictions of uncertainty and variability in physiological (blood flow and tissue volume) and drug specific (CL, fu,..) parameters on a target pharmacodynamic response (the brain receptor occupancy, considered as a surrogate marker of pharmacological drug activity) .
Methods:A WBPBPK/PD model was developed using animal and human blood flows and tissue volumes derived from the literature [1]. The whole body model consisted of nine tissue compartments and two blood compartments namely brain, lung, heart, gut, liver, kidney, muscle, skin, adipose, arterial and venous blood. Saturable liver metabolism was considered as the main elimination process. The impact on model PK/PD predictions of parameter uncertainty and inter-individual variability was assessed using Monte Carlo simulations. Different levels of inter-individual variability were explored assuming different statistical distributions of parameters using Berkeley Madonna software (version 8.0.1, University of California at Berkeley). For each evaluation, 1000 simulations were done: the results are presented as an average response with 95% prediction confidence intervals. The comparison of simulated and observed data was used to assess the consistency of the model predictions (plasma and brain drug concentrations in animal and plasma concentrations and brain receptor occupancy estimated in a PET experiment for human). Distribution, metabolism, absorption and pharmacodynamic data were the drug specific input parameters considered in the model. The tissue composition model was used to estimate the tissue: plasma partition coefficients under in vivo conditions [2]. Prior estimates of variability on model parameters were derived from published studies [3]. A PK/PD model based on a direct link between plasma/ brain and pharmacological effect was developed using a sigmoid- Emax model for animal: this was used to predict the brain receptor occupancy in man.
Results and conclusion:The proposed model accurately predicted the animal PK/PD response while the scaled model properly described the PK/PD observations in human. Furthermore, the incorporation of variability and uncertainty into PK/PD model parameters allowed the derivation of an accurate estimate of the inter-individual variability in human plasma concentration and receptor occupancy. The proposed WBPBPK/PD modeling strategy can be applied in early drug discovery, prior to in vivo study using in silico and in vitro data to predict plasma and tissue PK of drug candidates. This approach could also support a better mechanistic understanding of PK properties by developing mechanism-based PK/PD relationships from predicted tissue kinetic data. This would facilitate more rational decision making during clinical candidate selection, and the scaling up of PK and PK/PD relationships across species, routes of administration and dose levels.
References:
[1]Bernareggi, A. & Rowland, M. (1991) Pysiologic modeling of cyclosporin kinetics in rat and man. J. Pharmacokinet. Biopharm, 19, 21-50.
[2] Poulin, P. (1999) A priori prediction of Kp to facilitate the use of PBPK models. J. Pharm. Sci., 89, 16-35.
[3]Thomas, R. (1996). Variability in biological exposure indices using PBPK modeling and Monte Carlo simulation. Am. Ind. Hyg. Assoc. J. , 57, 25-32.

Cilomilast (Ariflo): Population pharmacokinetic modeling and validation in COPD patients.

J Aluri, B Zussman, J Sidhu, B Patel and D Boyle
Clinical Pharmacokinetics/Modelling & Simulation, GlaxoSmithKline, King of Prussia, PA, US and Harlow, UK
poster
Background:  Cilomilast (ArifloÒ ) is a potent and selective PDE 4 inhibitor currently under development for the oral treatment of chronic obstructive pulmonary disease (COPD). Cilomilast population pharmacokinetics (Pop PK) were characterized in COPD patients in 2 Phase III clinical trials using a sparse sampling paradigm in 681 patients. Cilomilast plasma concentrations (Cp) from a third Phase III study (n=366 patients) were used as an external validation dataset to assess the predictability of the developed Pop PK model .
Objective:  The overall objective of this analysis was to develop and validate a Pop PK model for cilomilast using data from 3 identical fixed dose studies in the Phase III program.
Methods:  Model development and validation was performed using NONMEM V. Both one and two compartment pharmacokinetic models were examined. The influence of various covariates were examined on cilomilast pharmacokinetics to account for variability in the population. Model validation was performed in 3 three ways: 1) Comparison of observed vs Bayesian estimates of Cp using the prior Pop PK model parameters; 2) Fitting the prior Pop PK model to the validation dataset and comparing parameter estimates with those obtained using the model building data set and 3) By performing a posterior predictive check (PPC). PPC was performed by simulating a total of 1000 Cp values for each time point at which a Cp was determined. The percentage of observed data falling within 5th-95th percentile was determined. 
Results:  A one-compartment PK model with first order absorption and elimination best described cilomilast pharmacokinetics. Of the covariates examined, body weight was the only significant descriptor of cilomilast CL/F and Vss/F. Results of model validation confirmed predictability of the Pop PK model. PPC analysis indicated that the percent of the observed Cp in the validation dataset lying within the 5th-95th percentile of the simulated Cp was 94.5%. 
Conclusions:  The population pharmacokinetics of cilomilast were characterized in COPD patients and identified body weight as the only influential descriptor of cilomilast CL/F and Vss/F. External validation demonstrated good predictive performance of the Pop PK model.

Population Pharmacodynamic Analysis of Glucose and Insulin levels Evaluated with a Hot Glucose Minimal Model, a Total Glucose Minimal Model, and an Insulin Minimal Model

B Mc Hugh (1), R Gieschke (1), M Karlsson (2)
(1) Division of Clinical Pharmacology, F. Hoffmann-La Roche, Basel, Switzerland; (2) Department of Pharmacology, Uppsala University, Sweden
poster
Objective: To investigate differences in plasma glucose and insulin levels between volunteers and patients in the absence of drug, i.e., the degree to which insulin effects glucose production/disposition and the degree to which glucose effects insulin secretion/disposition. Beta-cell dysfunction and insulin resistance associated with type 2 diabetes mellitus perturbs the glucose regulatory system, causing postprandial and possibly fasting hyperglycemia. Mathematical models have traditionally been used to investigate the glucose-insulin interaction because they allow a quantitative assessment of physiologically relevant regulatory parameters.
Methods: We implemented 2 Compartment Minimal Models (Cobelli, et al., 1997) in NONMEM for Hot Glucose (disposition), Total Glucose (production), and Insulin (interaction) and considered volunteer data from the literature (Vicini, et al.) and a subset of patient data from a newly developed insulin sensitizer (Hoffmann-La Roche). The subset consisted of pre-dose measurements from type 2 diabetic subjects and post-dose measurements from type 2 diabetic subjects that received placebo. In the insulin modified FSIVGT, a total of 300 mg per kg body weight of a glucose solution enriched with 13± 5% of a stable glucose label [6,6-2H2] was infused over a period of no more than 30 seconds and, starting 20 min after the glucose load, 0.05 U of insulin per kg body weight was administered over 5 min.
Results: Following the FSIVGT, insulin sensitivity was observed to be a factor of 3 lower in the diabetic patients, glucose production was seen to be suppressed in both the volunteers and the patients, and insulin secretion was seen to be virtually unaffected.
Conclusion: We determine how to glucose effects insulin secretion and how insulin effects glucose production. Future work will be directed toward the development of a mathematical description of the glucose/insulin interaction to allow, for example, simultaneous prediction of insulin and glucose levels in the presence of singly and multiply administered anti-diabetic drugs from various classes.
References:
[1] Cobelli C, Vicini P, Toffolo G and Caumo A. The hot IVGTT Minimal Models: Simultaneous assessment of disposal indices and endogenous glucose production. In. Pennington Center Nutrition Series Volume 7: The Minimal Model approach and determinants of glucose tolerance. Bergman RN and Lovejoy JC ed. Louisiana State University Press; Baton Rouge and London.
[2] Vicini P, Caumo A and Cobelli C. The hot IVGTT two-compartment minimal model: indexes of glucose effectiveness and insulin sensitivity. Modeling in Physiology, 1997; E1024-E1032.

Population Pharmacokinetic Study Of Fotemustine

Y Bourhis (1), A Iliadis (2), C Lucas (3), AB Depouilly (3), C Laveille (3), B Tranchand (1)
(1) Centre Léon-Bérard, Lyon, (2) Faculté de Pharmacie, Marseille, (3) I.R.I.S., Paris
poster
The main purpose of this study was to perform the pharmacokinetic modelling of fotemustine (MUPHORANâ) and to improve the pharmacokinetic and variability parameters estimation by introducing covariates into the model.
84 patients with various types of cancer (non Hodgkin lymphoma n=6, renal cell carcinoma n = 5, malignant glioma n=27, hepatocarcinoma n=2, colocarcinoma n=11, malignant melanoma n=13, myeloma n=20) were included in this multicentre study. Each patient was treated with one or two courses of intravenous fotemustine, given as a one hour constant-rate infusion (a total of 109 courses were administered). Depending on the tumour type, patients received either 100 mg/m²/week (conventional dose regimen) or 300-500 mg/m²/day for two consecutive days (high dose regimen).
2 to 13 blood samples per patient were collected at each course, and fotemustine was assayed in plasma by high performance liquid chromatography (limit of quantitation < 20 ng/ml).
The pharmacokinetic analysis was performed using NONMEM version V under VisualNM. The candidate covariates were age ([19;76] years), sex (54 males, 22 females, 8 unknown), weight ([46;95] kg), height ([149;190] cm), creatininemia ([26;112] µmol.l-1), serum urea nitrogen ([0.2;1.4] µmol.l-1). The tumor type was also considered.
We tested 2- and 3-compartment linear models, with additive, multiplicative, and mixed error model, using the First Order method. The inter-occasion variability was also taken into account.
The pharmacokinetics of fotemustine was best described by a 2-compartment linear model (ADVAN3 TRANS4) with a mixed error model. The overall mean clearance and volume of distribution values were estimated at 85.4 l.h-1 and 21.5 l, respectively with an important inter-individual variability (82% and 78% respectively). The introduction of the statistically significant covariates decreased the variability of the clearance from 82 to 44%, and of the volume of distribution from 78 to 46%. The inter-occasion variability was 27% for the clearance and 43% for the volume of distribution.
In this way, the clearance of fotemustine could be expressed as a function of sex, age, creatininemia, serum urea nitrogen, and tumor type. Volume of distribution was expressed as a function of age, serum urea nitrogen and tumor type.
This model will be used to analyse the plasma concentrations of children receiving high doses fotemustine in an on-going phase I/II study and to compare the pharmacokinetic parameters of this paediatric population with those of adults.

Modelling of biomarker response of naproxen in rats and humans

Dymphy Huntjens, Magret Blom-Roosemalen, David Spalding, Meindert Danhof and Oscar Della Pasqua
LACDR/ Pharmacology
poster
Introduction: Cyclo-oxygenase (COX) inhibitors are widely used to treat acute inflammation and pain. They act by inhibiting the activity of the COX enzyme, and consequently the formation of prostaglandins and thromboxanes. The enzyme exists in two isoforms, COX-1 and COX-2 and it is now widely believed that inhibition of COX-1 accounts for the side effects, whilst inhibition of COX-2 accounts for the therapeutic benefits. No direct correlation is observed between the pharmacokinetics (PK) in plasma and analgesic effects of COX-inhibitors in either humans or animals. A biomarker, reflecting a process on the inflammatory cascade, may enable the characterisation of this nonlinear relationship. Such a biomarker may also allow extrapolation and prediction from animals to humans. 
In this study, the effects of naproxen, a non-selective COX-inhibitor, on PGE&shy;2 inhibition, a biomarker for the selective effects on COX-2, were investigated in vitro in rats and healthy volunteers. Results were compared to in vivo concentration-PGE2 inhibition relationship of naproxen in rats.
Methods: In vitro study: In rats, blood samples were collected from the tail vein, wheras in healthy volunteers, blood samples were collected from the volar forearm. Samples were incubated with spiked concentrations of naproxen. PGE2 concentrations were measured by Enzyme Immuno Assay (EIA). In addition, protein binding of naproxen was measured by ultracentrifugation. In vivo study: Naproxen was administered intraperitoneally (2.5 and 25 mg/kg) to male rats. At regular time-intervals, blood was collected from the tail vein to determine PK in plasma and systemic PGE2 levels.
Results: The naproxen concentration-PGE&shy;2 inhibition relationship in vitro in rats and humans was modelled with the Hill model using non-linear mixed effect modelling. Inter-individual parameters were assigned to Imax&shy;, I0, IC&shy;50 and Hill coefficient. Naproxen was more potent in rats as compared to humans. No significant differences in Hill, I0 and Imax were found between rats and humans, which indicates identical mechanism of COX-2 inhibition of naproxen in rats and humans. 
Free fraction ranged from 1.9±0.2-12.9±1.3 % in rats, versus 0.4±0.3-1.8±0.4 % in humans. Differences in potency of naproxen between rats and humans could be explained by differences in protein binding.
Dose dependent PGE&shy;2 inhibition was observed in vivo after naproxen administration. These findings show direct correlation with in vitro data indicating the predictive value of the latter.
Conclusions: Model-derived parameters from PGE2 inhibition enables the characterisation of drug-effects in animals and humans. Protein binding accounts for differences in potency between rats and humans. In vitro findings of naproxen PGE2 inhibition correlate to in vivo data. 

An integrated model for data from a microdialysis experiment

Karin Tunblad, Margareta Hammarlund-Udenaes and Niclas Jonsson
Division of Pharmacokinetics and Drug Therapy, Uppsala University, Sweden
poster
Background: Microdialysis measures the unbound concentration of a drug in a specific tissue. The microdialysis probe is perfused with a Ringer solution, and dialysate samples are collected in intervals. Since there is a flow through the probe, the concentration in the dialysate will be a fraction of the true extracellular concentration. This fraction is the recovery.
Objectives: The aim of this study was to compare a new model for data from a microdialysis experiment to a previously used model. This is exemplified with morphine-6-glucuronide (M6G) data.
Methods: A CMA/12 microdialysis probe was placed in striatum, and a CMA/20 probe was implanted into the jugular vein of ten Sprague-Dawley rats. The recovery of the probes was estimated using retrodialysis by drug. M6G was administered as a 4-h exponential i.v. infusion aiming at 3000 ng/ml in blood. The experiment was repeated on Day 2 with the addition of probenecid. Fractions of dialysate were collected in 10-15 min intervals, and arterial blood samples (total concentrations) were drawn at predefined time points.
The modelling was performed in NONMEM using the first order conditional estimation method with interaction. In the previous modelling approach the average venous concentrations in each collection interval were corrected for the average recovery calculated from the retrodialysis period. Thereafter the arterial concentrations, corrected for the individual protein binding by comparing the unbound AUC in venous blood to the total AUC in arterial blood, were modelled. The analysis of the brain concentrations was conditioned on the individual parameters from the arterial analysis.
In the new approach the idea is to (i) model all the data simultaneously, i.e the recovery the venous microdialysis data and the arterial data, and (ii) to model the venous data as they were collected in intervals using an output compartment. This handling of the venous data is comparable with urine data, which also is collected in intervals. 
Conclusion: The advantage with the new modelling approach is that all data are described with a single model, that less assumptions has to be made and that it is now possible to simulate all the steps in a microdialysis experiment. The latter allows for rational study design optimisation.

Combined-PK-Analysis of a new compound exhibiting highly variable plasma profiles due to first pass metabolism

Delphine Martin, Roeline Jochemsen , Christian Laveille and Nicolas Frey
Institut de Recherches Internationales Servier, 6 place des Pleïades, 92415 Courbevoie cedex
poster
INTRODUCTION AND OBJECTIVES
The compound (S-X) is characterised by good absorption but a low bioavailability due to a saturable first-pass hepatic effect, which is responsible for the non-linear pharmacokinetics. S-X is rapidly metabolised by cytochromes P450, 1A2 and 2C9 and only 0.010% of the unchanged compound is eliminated in the urine. 
The objectives of this combined pharmacokinetic analysis are to estimate individual plasma pharmacokinetic parameters for S-X from all the plasma or saliva samples collected during the clinical development after repeated oral administration of SX in patients and to assess the influence of covariates (gender, dose, smoker, time of administration, ….) on these parameters.
METHODS
The first step: Development of a POP-PK model for phase I data
Plasma samples from six phase I studies with doses of 25 or 50 mg of compound S-X were pooled and analysed using NONMEM.
The second step: External qualification of the POP-PK model using phase II data
The plasma concentrations from a Phase II study were used for an external qualification test of the POP-PK model. The evaluation was assessed by using a maximum a posteriori Bayesian analysis (MAP Bayesian). 
The third step: Use of the POP-PK model to analyse phase III data and to identify factors predicting between subject variability. 
In phase III, only saliva samples were collected. Based on a linear relationship between plasma and saliva concentrations established previously from phase I data, plasma concentrations will be predicted and analysed using NONMEM. 
RESULTS
The first step:
A one-compartment model was found to adequately describe the data. The analysis was performed on log-transformed data in order to reduce the residual variability estimate, and also to avoid biased PRED vs. DV plots. A mixture model was used for the input phase in order to describe the complex input profiles observed in a subset of patients. The input phase was hypothesised to be composed of two types of processes: a first-order input, or a zero order input followed by a first order-input. A specific variability on the disposition parameters was defined in order to estimate the interindividual-variability of the first-pass effect.
The second step:
The agreement between the observed and predicted concentrations issued from the MAP Bayesian analysis was good, suggesting that the model may be considered preliminarily qualified.
The third step:
The third step is in progress and the results will also be presented at the PAGE meeting.

Modeling & Simulation Approach to Discriminate True Food Effects: Comparison with Standard Noncompartmental Methods

Sunny Chapel, PhD, Jeffrey S. Barrett, PhD, Marc Pfister, MD
Aventis Pharmaceuticals, Bridgewater, NJ, USA
poster
Objective: To explore differences in estimation methods to quantify food effect (FE) on absorption rate constant (Ka) between compartmental population modeling (CM) and noncompartmental methods (NCM). To test effects of model misspecification (fitting one-compartment model to two-compartment PK data), approximation methods (FO vs. FOCE interaction), fixed inter-individual variability of Ka, sampling schemes, number of patients, etc on the estimation performance.
Methods: One thousand six hundred FE 2-way cross-over trials were simulated using one-compartmental model with first order absorption. Sixteen trial designs were tested: 4 different sampling schemes (t-last 8, 12, 16, and 24h post-dose) and 4 different numbers of subjects (12, 18, 24, and 32 subjects/trial). FE on Ka (0 to 50%), Ka (1 to 6 times elimination constant) and interindividual variability on Ka (0 to 100%) were randomly assigned from uniform distributions. CM estimates for FE on Ka were compared with NCM. Prediction error (PE%) was calculated as 100(Estimated FE-True FE)/True FE.
Results: Regardless of trial design and approximation methods, CM resulted in |PE| >20% in less than 5% of trials. Model misspecification resulted in overestimated FE with PE >20% in more than 40% of trials. In contrast, NC Cmax ratios underestimated FE with PE <-20% in more than 90% of trials. With CM PE was not sensitive to trial design while NC tended to perform better with increased numbers of samples and subjects.
Conclusion: Compartmental population modeling is preferred to estimate the magnitude of FE on Ka. Model misspecification may significantly affect quantification of FE on Ka. The magnitude of FE on Ka estimated with NC Cmax ratios may be misleading. These results suggest that food effect labeling guidance may be inaccurate under certain conditions. These results must also be re-evaluated based on proposed exposure metrics, which may be more forgiving to noncompartmental methods.

Pharmacodynamic drug interaction of roxifiban during CYP induction and inhibition

Sy SK(1,2,3), Pieniaszek HJ(3,4), Kornhauser DM(3), Davidson AF(3), Jiao Q(3), Cain V(3,5), Martin DE(3,6)
1 Innaphase Corporation, Philadelphia, Pennsylvania, USA; 2 Center for Nonlinear Dynamics, Physiology, McGill University, Montreal, Quebec, Canada; 3 Bristol-Myers Squibb, Lawrenceville, New Jersey, USA; 4 HPP Consulting, Newark, Delaware, USA; 5 AstraZeneca, Newark, Delaware, USA; 6 Panacos Pharmaceuticals, Gaithersburg, Maryland, USA
poster
Objective: To investigate the cytochrome P450-modulated effects on the pharmacokinetics and pharmacodynamics of the active hydrolysis metabolite of roxifiban, XV459, through administration of ketoconazole, a potent CYP3A4 inhibitor, and rifampin, a non-specific inducer of CYP3A4. Since the biotransformation of roxifiban was thought to be solely mediated via ester hydrolysis forming XV459, the effect of induction and inhibition of CYP was initially hypothesized not to affect XV459 pharmacokinetics.
Methods: In a randomized, 3-way crossover study, a total of 6 healthy volunteers and 6 subjects with mild renal impairment received 1 mg roxifiban per day for seven days, either alone or in combination with 200 mg ketoconazole once-daily (administered 3 hours before roxifiban for 8 days) or 600 mg rifampin once-daily (administered 3 days before roxifiban for 8 days). Plasma pharmacokinetics of XV459 were assessed using steady-state non-compartmental method in the three treatment groups. Pharmacodynamic response was evaluated using percent inhibition of platelet aggregation and this response was correlated with pharmacokinetic concentrations using a mixed effect nonlinear regression model with creatinine clearance as a covariate of the model. Both model-independent analysis and population pharmacodynamic model were evaluated using Kinetica 4.1.
Results: Ketoconazole significantly decreased XV459 clearance by approximately 36% and 30% and increased the percentage inhibition of platelet aggregation from pretreatment baseline by 30% and 12% in both normal healthy volunteers and mild renally impaired subjects, respectively. CYP inhibition by ketoconazole also shifted the concentration-effect relationship towards increased EC50 by approximately 21%. Concomitant rifampin administration with roxifiban, on the other hand, increased the clearance of XV459 by 91% to 116% resulting in decreased XV459 systemic exposure by 45% and decreased antiplatelet activity by 8% to 21%. CYP induction by rifampin decreased EC50 by approximately 61%.
Conclusion: Concomitant administration of roxifiban with rifampin or ketoconazole produced unexpected changes in the pharmacokinetics of XV459 and significant alterations in antiplatelet activity. The population pharmacodynamic Emax model in Kinetica 4.1 provides a sensitive tool to detect such interaction.

Population Analysis of the Pharmacokinetics and the Haematological Toxicity of the Fluorouracil-Epirubicin-Cyclophosphamide Regimen in Breast Cancer Patients

Sandström M (1), Lindman H (2) , Nygren P (2), and Karlsson MO (1)
(1) Division of Pharmacokinetics and Drug Therapy, Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Sweden. (2) Department of Oncology, Radiology and Clinical Immunology, Uppsala University Hospital, Uppsala, Sweden.
poster
Objectives: The aims of the study were (i) to characterise the pharmacokinetics (PK), including inter-individual and inter-occasion variability as well as covariate relationships and (ii) to characterise the relationship between the PK and the haematological toxicity of the component drugs of the Fluorouracil (5-FU) - Epirubicin (EPI) - Cyclophosphamide (CP) regimen in breast cancer patients.
Methods: Data from 140 breast cancer patients were included in the analyses. The patients were all treated with the FEC regimen every third week for three to twelve courses, either in standard doses, i.e. 600/60/600 mg/m2 of 5-FU, EPI and CP, respectively, or according to a dose escalation/reduction protocol (tailored dosing). Pharmacokinetic data were available from 84 of the patients, whereas time-courses of haematological toxicity were available from 87 patients. The data analysis was carried out using mixed effects models within the NONMEM program.
Results: The PK of 5-FU, EPI and 4-hydroxy-cyclophosphamide (4-OHCP), the active metabolite of CP, were described with a one-compartment model with saturable elimination, a three-compartment linear model and a two-compartment linear model, respectively. No clinical significant correlation was found between PK across drugs. The unexplained variability in clearance was found to be less within patients, between courses (inter-occasion variability, IOV) than between patients (inter-individual variability, IIV) for EPI and 5-FU. For 4-OHCP the IIV diminished by one half when significant covariates were included and the final population model predicts an IIV that is equal to IOV. The time-course of haematological toxicity after treatment was well described by a semi-physiological model that assumes additive haematological toxicity between CP and EPI with negligible contribution from 5-FU. The influence of G-CSF could be incorporated into the model in a mechanistic manner as shortening the maturation time and increasing the mitotic activity.
Conclusions: The models presented describe the dose-concentration-toxicity relationships for the FEC therapy and may provide a basis for implementation and comparison of different individualisation strategies based on covariates, therapeutic drug monitoring and/or pharmacodynamic feedback. The pharmacodynamic model extends on previous semi-mechanistic models in that it also takes G-CSF administration into account.

Simultaneous Population D-Optimal Designs of Pharmacokinetic-Pharmacodynamic Experiments

A.C. Hooker, M. Dodds, and P. Vicini
Resource Facility for Population Kinetics, Department of Bioengineering, University of Washington, Seattle, Washington, USA
poster
Objectives:  Experimental pharmacokinetic-pharmacodynamic (PK-PD) data in the literature are commonly fit to population PK-PD models via simultaneous model fitting, where PK-PD parameters are all adjusted at the same time, based on both PK and PD measurements [4].  On the other hand, optimal design strategies are never computed using simultaneous population PK-PD models.  Simplifications of the simultaneous population design approach are used, including: (a) sequential individual-based [2], (b) simultaneous individual-based [1], and (c) sequential population-based PK-PD design optimization [3].  One could argue that these designs are all, in some sense, sub-optimal, if the data is to be fit using a more complicated simultaneous population PK-PD model.  The objective of this work was to compare standard optimal design practices with experimental designs that are computed in a manner consistent with the expected model fitting procedure.  Specifically, we calculate simultaneous population D-optimal designs of PK-PD experiments and compare these designs via simulation to the simplified experimental designs based on approaches (a)-(c).
Methods:  Taking published population PK-PD experiments, we compute simultaneous population D-optimal designs and D-optimal designs based on the simplified techniques (a)-(c).  D-optimal designs are computed by minimizing the determinant of the inverse of the Fisher information matrix of model parameters with respect to the design variables (the sampling times).  We then simulate numerous replicate experiments (using the assumed true parameter values) based on each D-optimal design.  From this simulated data pool, we then simultaneously estimate population PK-PD model parameters.  Then, we compare the parameter values, estimated conditionally on the above four designs, to the true parameter values via metrics such as percent bias and percent root mean square error. 
Conclusions:  Our preliminary results indicate that, even with many fewer samples per subject, population-based optimal designs will achieve similar or better parameter estimation accuracy compared to individually-based optimal designs.  One main advantage of population-based optimal designs appears to be that the number of sampling times in the designs can be less than the number of fixed effects in the model (the theoretical limit in individually-based designs).  However, in the limit of one sample per individual, the population D-optimal designs seem to be inadequate.  
References:
[1] C. Cobelli, A. Ruggeri, J. J. Distefano III and E. M. Landaw.  Optimal design of multioutput sampling schedules -- software and applications to endocrine-metabolic and pharmacokinetic models.  IEEE Trans Biomed Eng.,  32:249-56, 1985.
[2] Y. Hashimoto and L. B. Sheiner. Designs for population pharmacodynamics: value of pharmacokinetic data and population analysis. J. Pharmacokinet. Biopharm., 19:333-353, 1991.
[3] Y. Merl´e and M. Tod. Impact of pharmacokinetic-pharmacodynamic model linearization on the accuracy of population information matrix and optimal design. J. Pharmacokinet. Pharmacodyn., 28:363, 2001.
[4] C. Peck, R. Gieschke, and J. L. Steimer. Current status and future directions of PK/PD in drug discovery and development. In Measurement and kinetics of in vivo drug effects. Advances in simultaneous pharmacokinetic/pharmacodynamic modeling.  Part 1., pages 1-7, 2002. M. Danhof, M. Karlsson and R. J. Powel editors.

Population pharmacokinetic/pharmacodynamic modelling of the haematological effects of the new anticancer drug diflomotecan: A combined analysis from the first two phase I studies

MJ. Garrido(1), JM. Cendrós(2), IF. Trocóniz(1), C. Segura(1), C. Peraire(2), R. Obach(2)
(1) Department of Pharmacy, School of Pharmacy, University of Navarra, Pamplona 31080, Spain; (2) Metabolism and Pharmacokinetic Service, Research Department, Ipsen Pharma S.A., Carretera Laureá Miró, 395, Sant Feliú de Llobregat 088980, Barcelona, Spain.
poster
Purpose: To develop a population pharmacokinetic/pharmacodynamic (pk/pd) model of diflomotecan to assist in the dosing and blood sampling strategies in future Phase II clinical trials.
Study design: Data from two studies were combined. 24 cancer patients were involved in the 001 study. Subjects received diflomotecan as a 20 min i.v. infusion administered every three weeks at doses (mg/m2) of 1 (n=1), 2 (n=2), 4 (n=13), 5 (n=4), 6 (n=3), and 12 (n=1). The number of cycles varied from one to six. Diflomotecan was measured in plasma after the first administration for a period of two days. Neutrophil counts in peripheral blood were followed every 3-4 days for the entire course of the trial. In study 700, 24 cancer patients received the drug in a 20 min i.v. dose of 0.1 (n=6), 0.2 (n=12) or 0.27 (n=6) mg/m2. After a period of two weeks, diflomotecan was given orally once daily for five consecutive days at the following doses: 0.1 (n=3), 0.2 (n=4), 0.27 (n=11), or 0.35 (n=4) mg/m2. Blood samples for pk characterisation were taken during the first two and last cycles. Neutrophil counts were measured every 5-6 days. 
Data analysis: The population pk/pd model was derived from a total number of 876 and 1214 plasma levels and neutrophils counts, respectively. The analysis was performed with NONMEM version V. Pk was described with standard absorption and disposition models. Both, inter- and inter-occasion variability were explored in all the parameters. Time course of neutropenia was modelled using a semi-physiological model.[1]
Results: Drug absorption and disposition were best described with a first order and a three compartmental model, respectively. The estimates of plasma clearance and oral bioavailability were 525 L.day-1 and 0.66, respectively. Both parameters showed inter-subject (65 and 26 %) and inter-occasion (23, and 23 %) variability. None of the demographics tested elicited significant covariate effects (P > 0.05). The estimates of the system dependent parameters resembled the ones previously reported, and diflomotecan exerted a linear plasma concentration dependent and reversible inhibition of the rate of synthesis of proliferative cells.
Conclusion: Regarding its pk characteristics diflomotecan behaves linearly with time and over a wide range of doses. The haematological toxicity induced could also be described. Therefore information from this first modelling exercise can be used to explore the outcome of future studies.
References:
[1] Fibreg LE, Henningsson A, Maas H, Nguyen L and Karlsson MO. Model of chemotherapy-induced myelosupression with parameter consistency across drugs. J Clin Oncol 20: 4713-4721; 2002.

Influence of study design and interindividual variability on In Vitro - In Vivo Correlation evaluation

Zamacona MK, Gomeni R
GlaxoSmithKline, Clinical Pharmacokinetics Modelling & Simulation, Verona (Italy)
poster
Background. Although crossover studies are preferred to establish In Vitro – In Vivo Correlations (IVIVC), parallel studies are also acceptable if a common reference treatment is used 1. The outcome of an IVIVC may be influenced by the experimental design and by the extent of inter- individual variability on the drug absorption/disposition kinetic properties of the compound.
Objective. To investigate the influence of the study design and inter-individual variability in the outcomes of a Level A IVIVC. 
Methods. Plasma concentration time profiles following oral administration of three formulations (slow, medium and fast release) and after intravenous administration were simulated assuming a crossover design. A one- compartment model with first order absorption and elimination was used. Plasma concentration time profiles were simulated using NONMEM with different degrees of interindividual variability and measurement error. Two sets of simulations were produced: with bioavailability fixed to one and no inter-individual variability; and with bioavailability of 0.8 and an inter-individual variability low and high. The percentage of in vivo drug absorbed vs. time was calculated using numerical deconvolution from the simulated oral plasma concentration time profiles by using the intravenous data as unitary impulse response function. Individual profiles were used to compute the corresponding individual absorption profiles. A linear regression analysis was done to evaluate the degree of correlation between in vitro dissolution and in vivo release profiles. Internal predictability analysis was done to evaluate the accuracy of the In-Vivo predictions given the In-Vitro dissolution data. Mean absorption profiles for each formulation were used in the convolution step to predict the plasma concentration time profiles. Cmax and AUC values were estimated for the simulated and predicted profiles and the prediction error was calculated. In a subsequent analysis, the mean profiles in the deconvolution step with a common unitary impulse response function were used in the analysis to mimic the scenario of a parallel rather than a crossover design. 
Results and conclusions. Crossover designs resulted always in good predictability but prediction error slightly increased when the increase of inter-individual variability. Parallel designs gave also in general good predictability values, but with prediction error higher than crossover designs. 
References. 
[1] Guidance for Industry: Extended release oral dosage forms: Development, evaluation, and application of in vitro/in vivo correlations. US Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research. September 1997. 

Modeling the longitudinal concentration-response data after i.m. administration of Risperdal CONSTATM in psychotic patients of different phenotypes

An Vermeulen Ph.D., Vladimir Piotrovsky Ph.D.
Johnson & Johnson Pharmaceutical Research & Development
poster
Introduction: A depot injectable formulation of Risperidone (RIS, Risperdal CONSTATM) for i.m. administration once every two weeks has been developed and is on the market in quite a few countries now. The formulation is an aqueous suspension of RIS encapsulated in microspheres, which are composed of a biodegradable copolymer of poly-(d,l-lactide-co-glycolide). Polymer erosion controlles the release of risperidone.
The phase 3 clinical development program for this formulation included two efficacy trials: one double-blind trial (USA-121) and a non-inferiority trial (INT-61). The efficacy was evaluated using the Positive and Negative Symptoms Scale or PANSS. 
RIS is mainly metabolised by CYP2D6 to the active metabolite 9-hydroxy-risperidone. The sum of RIS and 9-hydroxy-risperidone constitutes the 'active moiety' (AM) and is responsible for the improvement in PANSS score. 
Objectives: The objectives of the current population analysis were: 
to model the pharmacokinetics of RIS and the AM in subjects of different phenotypes (USA-121);
to model the treatment efficacy (improvement in PANSS scores) in terms of steady-state AM plasma concentrations (USA-121); 
to check the robustness of the PK-efficacy model by simulating the outcome of the non-inferiority trial (INT-61). 
Methods and results: Two population PK models were developed using USA-121 data: one for RIS and the other for the AM. Since the activity of CYP2D6 is subject to genetic polymorphism, the population is divided in poor, intermediate and extensive metabolisers, and this was taken into account in the RIS model.
The models included a one-compartment disposition submodel characterized by clearance and volume of distribution and three parallel absorption pathways: an immediate pathway describing the absorption of non-encapsulated risperidone, and fast and slow sustained-release pathways. At the first stage, individual estimates of RIS and AM clearances together with other model parameters were obtained using data-rich trials. These estimates were summarized, and typical values and IIV were derived and further used as priors to obtain individual posterior clearance estimates for patients of sparse-data trials via a Bayesian procedure. 
Individual clearances were then used to calculate model-predicted steady-state concentrations of the AM in USA-121, which were fed into a dynamic (indirect-response) population PK-efficacy model. It was based on the idea that the rate of increase and decrease of response determines its actual value. The concentration-response model has the following parameters: the PANSS score at patient inclusion, the PANSS score to be ultimately achieved due to disease progression, placebo and risperidone treatment, the rate constant of re-establishing the balance after a change in condition and the time to drop out. The effect of the AM was implemented as an Emax model.
The final population PK-efficacy model was used consecutively to simulate the INT-61 trial.

A Population Pharmacokinetic-Pharmacodynamic Model For Count Data: Application to the Effect of Atosiban on Uterine Activity in Preterm Labor Patients

Eugène Cox (1), Henrik Agerso (2), Thomas Senderovitz(2).
(1)Pharsight Corporation, Mountain View, USA; (2) Ferring Pharmaceuticals A/S, Copenhagen, Denmark.
poster
Objectives: The objective of this study was to quantify the relationship between drug exposure and the inhibitory effect of the oxytocin antagonist atosiban on uterine contraction rate in women with pre-term labour. 
Methods: Atosiban was administered to women with preterm labor at different dose levels as a single dose subcutaneous injection in a randomized, double-blind, placebo controlled, parallel study manner. The Uterine Contraction Rate (UCR) were recorded at 1-hour intervals up to 12 hours after drug administration using a tocodynamometer. Serial venous blood samples were collected and assayed for atosiban concentrations in order to determine the pharmacokinetic profile of atosiban. Uterine contractions rates were then related to plasma concentrations in order to quantify the in vivo pharmacodynamic profile of atosiban. 
Results: Pharmacokinetic data were analyzed for each individual patient on the basis of a one-compartment pharmacokinetic model with first order absorption from the injection site. The mean (± SEM) values of clearance, volume of distribution and absorption rate for atosiban were 32± 0.2 L/hr, 46 ± 0.1 L and 7.5 ± 0.2/hr, respectively. A profound hysteresis was observed in the relationship between atosiban plasma concentrations and UCR and this hysteresis was accounted for using an effect compartmental model. The actual observed UCR was then related to the effect site concentration using a population pharmacodynamic model for count data assuming a Poisson distribution of the observed UCR. The estimate of the concentration that results in 50% of the maximal atosiban-induced reduction of UCR (EC50) was. 37± 2 ng/ml. The interpatient variability of the mean UCR value was estimated to be 8%. Also, a profound placebo response was observed during the time course of the study. Apart form standard diagnostic procedures, the model was further validated on the basis of a posterior predictive check.
Conclusion: The results of this study show that the in vivo pharmacodynamic action of atosiban can be adequately quantified on the basis of a population PK/PD model for UCR in patients with preterm labor.

Pharmacokinetics of Daunorubicin and its metabolite Daunorubicinol in the absence and presence of a potent P-gp inhibitor, Zosuquidar.3HCl (LY335979).

Sophie Callies 2, Dinesh P de Alwis 1, Michael Burgess 1, and Leon Aarons 2
1Eli Lilly and Company Limited, Surrey, U.K.
poster
Objectives: Clinical investigations have shown that P-glycoprotein inhibitors dramatically decrease the systemic clearance of co-administered oncolytics. The potential impact of zosuquidar.3HCl, a potent inhibitor of the P-gp efflux transporter on the pharmacokinetics (PK) of daunorubicin (DAUN) and its metabolite daunorubicinol (DAUNOL) was examined in a phase I dose escalation trial using a population approach. In addition, a relationship between plasma concentrations of Zosuquidar.3HCl and P-gp inhibition as measured ex vivo was determined.
Methods: The pharmacokinetics of DAUN and DAUNOL were studied following two sequential administrations: on day 1, patients received DAUN (50 mg/m2 IV over 10 min) alone and on day 3, patients received Zosuquidar.3HCl IV (200 or 300 mg/m2 over 6 h or 400 mg 3 h) and DAUN, administered as previously, 1 and 0.5 hour after the start of the 6 and 3 hour infusion of Zosuquidar.3HCL, respectively. A total of 16 patients with acute myelogenous leukemia (AML) or myelodysplastic syndrome (MDS) were enrolled.
Results: A three-compartment PK model adequately described the DAUN concentration time profiles. A five compartment or a four compartment pharmacokinetic model adequately described the combined DAUN-DAUNOL PK profiles in the absence or presence of Zosuquidar.3HCl, respectively (three compartment for DAUN and two or one compartment for DAUNOL). The additional distribution compartment for DAUNOL permitted the model to fit adequately the two peaks observed in DAUNOL PK in the absence of Zosuquidar.3HCl.
The overall impact of short IV infusion of Zosuquidar.3HCL (6 h or less) on coadministered DAUN was minimal with an approximately 10 % reduction in DAUN clearance (CL). The population model predicted a 50 % decrease on DAUNOL apparent clearance (CL/fm) in the presence of either a 3 h or 6 h infusion of Zosuquidar.3HCl.
Pharmacodynamic measurements of inhibition of Rhodamine 123 P-gp-mediated-efflux in CD56 lymphocytes, showed that the Zosuquidar.3HCl dosing schedules administered in this study lead to maximal P-gp inhibition. A direct reversible concentration-effect relationship between Zosuquidar.3HCl plasma concentrations and inhibition of Rhodamine efflux in CD56 lymphocytes was defined by a sigmoid Emax model. The IC50 was 31.6 +/- 12.0 µg/L. Plasma concentrations in excess of the IC90 (172.4 µg/L) were readily achieved during 6 h and 3 h infusions of zosuquidar.3HCL and provided maximal P-gp inhibition during the distribution phases of DAUN.
Conclusions: Both infusion regimens of zosuquidar.3HCL provided maximal P-gp inhibition. The decrease in DAUN CL (10 %) and DAUNOL CLm/fm (50 %) in the presence of zosuquidar.3HCl likely reflects inhibition of P-gp by zosuquidar.3HCl in the bile canaliculi impeding biliary excretion of DAUN and DAUNOL. The results reported in this study need to be interpreted carefully due to the sequential nature of DAUN administration and analysis. It is critical to assume that both DAUN and DAUNOL PK are concentration and time independent. A randomised study is currently ongoing to assess the validity of this hypothesis and confirm these research findings.

Application of population approaches in pharmaco-toxicological studies

M. Simeoni(1), F. Fiorentini (2), M. Germani(2), I. Poggesi(2), M. Rocchetti (2)
(1) Dipartimento di Informatica e Sistemistica, Pavia University, Pavia, Italy (2) Global Drug Metabolism, Pharmacia, Nerviano, Italy
poster
Objectives:In a typical toxicokinetic program, the pharmacokinetic information is obtained from different studies characterized by a limited number of observations (in terms of number of experimental units and plasma samples/experimental unit). The possibility of performing meta-analyses as soon as new data are becoming available during the development of a new drug is one of the most interesting application of the population pharmacokinetic analysis. In this communication, this approach was applied to a real toxicokinetic program, in which resampling was applied to one of the studies to simulate a sparse sampling strategy. 
Methods: Two toxicity studies of a new intravenous anticancer drug were retrospectively considered: a single and a cyclic dose study. A 2-compartment model with elimination from the central compartment and a model of errors including random effects and fixed effects for gender, dose and cycle was used. Two population analyses were performed using NONMEM: in the first case both the complete data sets from the two studies were considered; in a second analysis only the complete data set of the single dose study and a subset (approximately 10%) of the data in the cyclic study were used. The results of both population analyses were compared with those obtained from a conventional non-compartmental analysis performed on the two complete data sets.
Results: The results obtained from the two different population approaches were in excellent agreement. Compared with the non-compartmental approach, both population analyses gave similar results in terms of average pharmacokinetic parameters. Similar conclusions were also obtained in terms of dose-, time- and gender-dependencies.
Conclusion: Overall, population approaches can be efficiently applied to preclinical programs, allowing the incorporation into the models of the growing body of preclinical information. With some prior knowledge, such as that obtained in the first studies, sparse sample analysis can be applied in a toxicokinetic program, with a consequent substantial reduction of costs.

A Bayesian approach to non-parametric AUC estimation in population studies

P. Magni(1), R. Bellazzi (1), G. De Nicolao(1), M. Simeoni(1), M. Germani(2), I. Poggesi(2), M. Rocchetti (2)
(1) Dipartimento di Informatica e Sistemistica, Pavia University, Pavia, Italy (2) Global Drug Metabolism, Pharmacia, Nerviano, Italy
poster
Objectives: In cases in which frequent and/or fixed individual samplings cannot be applied due to ethical, technical and cost reasons, the use of the trapezoidal rule for AUC calculation is impossible or can give unreliable results. Anyway, having also in these cases a sensible estimate of the systemic exposure is of great interest. Non-linear mixed effect models can provide both population and individual estimates of AUC based on sparse sampling protocols; however, the knowledge of the structural model of pharmacokinetics is required. This could not always be available, especially in the first phases of preclinical development. In this work, we propose and evaluate a new nonparametric Bayesian scheme for AUC estimation in population studies with arbitrary sampling protocols, without the need of structural pharmacokinetic models. 
Methods: The individual plasma concentration curves and the mean population curve are described by a random walk process, in which the only requirement is a certain degree of regularity of the time profiles. Population and individual AUC estimation are performed by numerically computing the posterior expectation through a Markov Chain Monte Carlo algorithm.
Results: The method was applied to simulated and real data sets. The methodology was not only able to provide good estimations of the average population AUC and its variability, but also to provide these estimation for the individual AUCs. This was possible also in cases in which samples were sparse and/or obtained at different sampling times in the different experimental units. 
Conclusion: This work presents a new Bayesian approach to nonparametric AUC estimation in population studies. The method is of interest when no reliable structural model is available to describe the kinetics of the substance under analysis. The new method has wider applicability and gives better results than other nonparametric approaches (Bailer, and Yeh) and allows for arbitrary sampling and in the case of misspecified models does even better than the standard parametric approaches.

Simultaneous Population Pharmacokinetic Model of AQUAVAN™ And AQUAVAN™-Derived Propofol

Leonid Gibiansky (1), Michel MRF Struys (2), Ekaterina Gibiansky (3)
(1) Emmes Corporation, Rockville, MD, USA; (2) Dep. of Anesthesia, Ghent University Hospital, Gent, Belgium; (3) Guilford Pharmaceuticals, Baltimore, MD, USA
poster
Background: Propofol, an intravenous anesthetic agent, is used for the induction and maintenance of general anesthesia and sedation. Infusion of propofol emulsion results in rapid onset and offset of anesthesia, which makes it a widely used agent. AQUAVAN™ (GPI 15715), a water-soluble prodrug of propofol, eliminates the emulsion related disadvantages of the current propofol formulation. In addition, AQUAVAN™ provides a more gradual onset and offset of action, which is beneficial in some settings; e.g., short-term sedation where it may be administered as an injection. Preliminary investigations revealed a non- linearity of AQUAVAN™ -derived propofol pharmacokinetics; therefore, it is vitally important to develop a PK model that can be used to optimize dosing and predict results of future studies.
Objectives: To develop a population PK model of AQUAVAN™ and AQUAVAN™- derived propofol over a wide range of doses (from light sedation to induction of anesthesia) .
Methods: Arterial plasma samples from a dose ranging study (5 to 30 mg/kg) of AQUAVAN™ administered as a bolus to 36 healthy volunteers were collected and analyzed. Rich plasma concentration/time data in the interval from 1 to 480 minutes post dose were available for both AQUAVAN™ and AQUAVAN™ -derived propofol. The simultaneous population PK analysis was performed using NONMEM. The influence of weight and gender on exposure was examined. Bootstrap and leverage analyses were used for model evaluation.
Results: AQUAVAN™-derived propofol pharmacokinetics was described by a nonlinear six-compartment model. AQUAVAN™ elimination was described by linear elimination and nonlinear metabolism to propofol. The rate of metabolism increased with AQUAVAN™ concentration, possibly due to saturation of protein binding. Propofol pharmacokinetics was described by linear elimination and saturable distribution. Weight influenced kinetics so that slightly less than weight-proportional dosing provided weight-independent exposure.
Conclusions: A predictive population PK model of AQUAVAN™-derived propofol was developed for a wide range of doses. The model suggested an explanation for the unique pharmacological profile of Aquavan administered as a bolus: rapid initial rate of metabolism slowing with falling Aquavan concentrations provides rapid onset of action and gradual offset. The model confirmed the adequacy of weight-adjusted dosing, and the absence of gender influence on AQUAVAN™-derived propofol exposure. The model was used for PK/PD modeling and for guiding dosing paradigm in a Phase II study.

Bispectral Index of AQUAVAN(tm)-Derived Propofol: Population PK/PD Modeling and Application to an Effect - Controlled Trial

Ekaterina Gibiansky (1), Michel MRF Struys (2), Leonid Gibiansky (3)
(1) Guilford Pharmaceuticals, Baltimore, MD, USA; (2) Dep. of Anesthesia, Ghent University Hospital, Gent, Belgium; (3) Emmes Corporation, Rockville, MD, USA
poster
Background: Propofol is an intravenous sedative-hypnotic agent used for the induction and maintenance of general anesthesia, and sedation. AQUAVAN≥ Injection (GPI 15715) is a water-soluble prodrug of propofol. Preliminary investigation revealed that the PK and PK/PD of AQUAVAN≥ -derived propofol and propofol from the current lipid emulsion formulation are different. Our goal is to predict the pharmacodynamic effect of AQUAVAN≥ Injection over a wide range of doses (light sedation to induction of anesthesia).
Objectives: (1) To develop a predictive population PK/PD model of AQUAVAN≥-derived propofol.(2) To use the model for design of a Phase II, effect - controlled study of sedation during colonoscopy.
Methods: (1) A population PK model of Aquavan based on the rich data of 36 volunteers (single bolus doses 5-30 mg/kg) was used to predict individual propofol plasma concentrations. These predictions, coupled with the Bispectral Index (BIS, an EEG measure of sedation) data were used to establish the PK/PD model. The population PK and PK/PD models were combined into a simultaneous PK/PD model. Simulations, bootstrap, and leverage analyses were used for model evaluation.(2) In the planned study, AQUAVAN≥ Injection was to be administered as a bolus with supplemental doses administered if needed, based on the depth of sedation. The dosing regimen design was chosen based on study simulations, varying both initial and supplemental doses and the dosing interval. Model development and simulations were performed using NONMEM. 
Results: (1)BIS change from baseline was described by a Hill function of propofol concentration in the effect compartment. The rate constant of the effect compartment was proportional to propofol plasma concentration. Neither weight nor gender affected the PK/PD relationship.(2) Clinical trial simulation predicted that an initial bolus of 10 mg/kg followed, if needed, by 5 mg/kg three minutes later, would provide an adequate sedation to 97% of patients. Of these patients, 50% would not require the supplemental dose to attain sedation. 
Conclusions: A predictive population PK/PD model was developed over a wide range of doses. Doses pre-elected to produce the desired level of effect (light sedation to induction of anesthesia) were identified. The simulations confirmed the feasibility of using bolus doses of AQUAVAN≥ Injection to achieve and maintain sedation for short (20 √30 minutes) diagnostic and therapeutic procedures. The model-based clinical trial simulation was used to guide the dosing design of the sedation effect-controlled trial in patients.

Impact of slow receptor binding kinetics and change in Cerebral Blood Flow in receptor occupancy estimation with PET experiments. A simulation study

Stefano Zamuner and Roberto Gomeni
GlaxoSmithKline - Clinical PK/Modelling and Simulation, Verona, Italy
poster
Background: 11C is the most used labelling ligand despite its short half life (20 min). As a consequence no more than 90 minutes of PET scans can be followed because of tracer degradation. This limitation may constitute a relevant issue in the assessment of receptor occupancy in the presence of slow ligand-receptor kinetics.
Objectives: Assess the impact of possible bias in the estimation of 90% receptor occupancy after drug challenge when 90 minutes vs 240 scan time is considered for a compound showing slow ligand-receptor kinetics. The simulation study conducted also aimed to evaluate the impact of increasing measurements error, variability (inter and intra subject) and change in cerebral blood flow.
Methods: Reference time activity curves were generated using a standard compartmental model for ligand-receptor binding [3]. The model accounted for arterial input function, cerebral blood flow influence [4,5] and ligand-binding parameters (kon, koff, Bmax). A slow ligand-receptor dissociation was considered (kon = 0.04 min--1, koff = 0.008 min--1, Bmax = 1 nM) compared with other well characterised data from 90 minutes PET scans ([11C]FLB 457: kon = 0.05 and koff = 0.05, ([11C]raclopride kon = 0.01 and koff = 0.1). In the simulation study, the equilibrium condition of the tracer was not properly reached in 90 minutes. Data were generated up to 240 min following tracer and cold treatment in 40 subjects, considering a measurement error of 2-5%, an intra-subject variability of 5-15% and inter-subjects variability of 10-30%. The impact of a 50% change on cerebral blood flow on the binding parameters was evaluated. Binding parameter estimates were obtained using both arterial input model [1] and simplified reference tissue model [2] based on the presence of a region without specific receptors. The criterion used to evaluate the results was based on the quantification of bias. All the analyses were made using NONMEM V.
Results: No bias was observed in both models using the entire data set (measurement up to 240 minutes). A statistical significant bias was observed using data up to 90 min irrespective of the model used. The bias increased with both the measurements error and the inter-intra subject variability. In any case, the range of bias in RO estimation (90%) was negligible (0.17- 1.73%). No change in the binding parameters and RO estimation with an increase of cerebral blood flow (50%) was observed.
Conclusions: The simulation study indicated that, despite the presence of bias, the RO estimation, in a full occupancy scenario, was not significantly affected (
References: 
[1] Perlmutter et al. J Cereb Blood Flow Metab. 1986; 6:154-69.
[2] Lammertsma et al. Neuroimage. 1996; 4: 153-8.
[3] Mintum et al. Ann. Neurol. 1984; 15:217-227.
[4] Crone. Acta physiol scand. 1964; 58: 295-305.
[5] Renkin. Am J Physiol. 1959; 197:1205-1210.

Altered effect and pharmacokinetics of propofol in rats with experimental diabetes mellitus

Nerea Leal(1), Monica Rodriguez(1), Rosario Calvo(1), Fatima Agrad(1), Leire de la Fuente(2), Elena Suarez(1), John C Lukas(3)
(1)Department of Pharmacology, School of Medicine, University of the Basque Country, Leioa, Spain; (2)PharmaDatum, Edificio BEAZ, Sangroniz, Sondika; (3)Department of Pharmacy, Laboratory of Pharmacokinetics and Biopharmaceutics, University of Athens, Athens, Greece.
poster
Background: Propofol shows large variability in the hypnotic dose that may be due to pharmacokinetic and/or pharmacodynamic alterations caused by pathologies, so possibly also by diabetes mellitus (DM). The authors tested the influence of iatrogenic DM in the animal model in the induction dose and the time to the same endpoint (hypnosis) was lower in DM but the observed weight loss and alterations in the binding ratio explained the difference only partially. The pathology of the disease is known to include physiological changes in membrane permeability and metabolism among others and this remains undetermined.
Purpose: The pharmacokinetics and pharmacodynamics of propofol were studied in the DM rat model in order to elucidate the observed differences at induction of the hypnotic effect.
Methods: Diabetes was induced in rats (n = 10) by 60 mg/kg i.p. streptozotocin. Control rats (n = 8) received vehicle i.p. Glucose, cholesterol, triglycerides and albumin levels were determined in all animals. To study the pharmacokinetics, propofol was administered at 6 mg/kg/min for 2 minutes and 11 to 12 arterial blood samples were taken between 2.5 and 540 min and assayed for total propofol by HPLC. Bi and tricompartmental models were used with the FOCE method in NONMEM to analyze the observations. The -2LLD objective function difference at the 7.5 (p < 0.005) level, the SE estimates and residual plots were the criteria for model development.
Results: The pharmacokinetics differed structurally between control and DM rat groups. A bicompartmental description optimally explained kinetics under DM while a tricompartmental model described the observations in controls. In DM, central clearance was (mean [intercompartmental CV%]) CL = 0.024 L/min (61%), central volume, Vc = 0.2 L (45%), intercompartmental clearance, Q = 0.01 L/min (42%) and peripheral volume, Vt = 0.83 L (no CV estimate). In controls, CL = 0.028 L/min (28%), Vc = 0.24 L (11%), Q1 = 0.045 L/min (56%), V2 = 0.26 L (8%), Q2 = 0.034 L/min (31%), V3 = 5.49 L (no CV estimate). 
Conclusions: The kinetics of propofol in rats is altered by diabetic disease hence the initial distribution and elimination phases, of primary interest in anesthesia, differ. It may be of interest to perform studies in humans. We are in the process of analyzing the pharmacodynamics and covariate relationships in rats. The population distributions can be utilized to explore dosing protocols via simulation.

Modelling of the tolerance, rebound and carry-over phenomena observed in clomethiazole-induced hypothermic effects in rats.

Sandra A.G. Visser(1), Susanna Pozarek(1), Tomas Forsberg(2), Johan Gabrielsson(1).
AstraZeneca R&D Södertälje, DMPK & Bioanalytical Chemistry (1) and General Pharmacology (2), SE-15185 Södertälje, Sweden
poster
Objectives: Clomethiazole (CMZ) enhances g-aminobutyric acid (GABAA) receptor activity and is used as a sedative, hypnotic and anticonvulsant drug. In several animal stroke models, CMZ is also effective as a neuroprotectant, reducing ischemia- induced cerebral damage and behavioral abnormalities in rodents and primates. CMZ has been shown to induce dose-dependent hypothermia in rats and the difference between doses producing neuroprotection and doses causing hypothermia was established as part of the safety evaluation of the compound. In the present investigation, the onset, intensity, and duration of hypothermia, and the rebound hyperthermic effects of CMZ were studied in rats. 
Methods: The hypothermic effects of CMZ were studied in male Sprague Dawley rats after subcutaneous (sc) bolus administration of 0, 15, 150 and 600 µmol/kg and 24h continuous administration of 20 and 40 µmol/kg/h using osmotic pumps. Temperature was recorded using radiotelemetric transmitters between 4 days before dosing and 4 days after dosing. Plasma exposure to CMZ was obtained in different groups of (catheterized) rats with simultaneous temperature recording. 
Results: All animals displayed asymmetric circadian variation of 1 C in their baseline body temperature. A dose-dependent decrease in temperature was observed upon bolus sc dosing followed by a rebound hyperthermic effect upon returning to predose baseline. In the 24h sc infusion groups, a decrease in temperature was observed for the first 6-10 hour. The effect then returned to baseline in spite of continuous exposure to CMZ, indicating tolerance. A rebound hyperthermic effect was observed, which lasted for several days during daytime but not nighttime. 
Conclusions: The PK analysis showed that CMZ displays Michaelis-Menten kinetics. PD analysis showed a rapid lowering (onset) of body temperature that reached about 3 C reduction (intensity), and tolerance development (duration) of response in spite of the fact of continuous exposure to CMZ. A rebound hyperthermic effect was observed during daytime but not nighttime. 

Randomized dose ranging trials; assessment of statistical power for various design and analysis strategies

Kristin Karlsson, Mats O. Karlsson, Anders Grahnén and E. Niclas Jonsson
Uppsala University, Sweden
poster
Background: Historically the most used clinical trial design to describe the effectiveness of a drug is the randomized dose-controlled clinical trial (RDCT). About a decade ago an alternative to the RDCT was introduced; the randomized concentration-controlled trial (RCCT) design [1]. Contrary to the RDCT, the RCCT consider the pharmacokinetic variability and is suggested to be used to characterize exposure-response relations to achieve a theoretical gain in statistical power. However, it has been shown that the gain in statistical power with the RCCT design is model dependent [2].
Aim: To investigate, from a power point of view, the hypothesis that the most beneficial trial design and analysis strategy is to randomize as far as possible from, and use an independent variable as close as possible to the clinical endpoint in the mechanistic pathway of drug response.
Methods: The hypothesis is tested using simulations where the basic setup consists of a one compartment pharmacokinetic model at steady state conditions and a sigmoidal Emax pharmacodynamic model. The studies are simulated with randomization schemes on dose (RDCT) and concentration (RCCT), and the analysis of the data is performed with dose and concentration as independent variables, respectively. The significance criterion used for the statistical power of the studies is the log-likelihood ratio test. All the simulations and the analyses were made in the NONMEM software.
Results: The RDCT with concentration as the independent variable in the analysis yield the greatest power followed by the RCCT with concentration as the independent variable in the analysis.
Discussion: Our hypothesis seems to hold under the simulation conditions used. Real-life factors that may influence this result are: correlation between pharmacokinetic and pharmacodynamic parameters, patient drop-outs and model misspecification or complexity. Another real-life factor that may influence the randomization scheme, from a side-effect perspective, is safety, i.e. it may be necessary to have close control of the drug concentration levels that patients are exposed to and this may necessitate an RCCT design despite its expected lower statistical power.
References:
[1] Sanathanan LP, Peck CC. The randomized concentration-controlled clinical trial: an evaluation of its sample size efficiency. Control Clin Trials 1991;12:780-94.
[2] Endrenyi L, Zha J. Comparative efficiencies of randomized concentration- and dose-controlled clinical trials. Clin Pharmacol Ther 1994;56:331-8.

Meta analysis and clinical trial simulation in drug development.

Daren J Austin and Ann Allen
Clinical Pharmacokinetics/Modelling & Simulation, GlaxoSmithKline, Greenford, UK.
poster
Background: GSK123 is a potent and novel selective adenosine agonist under development for the inhaled treatment of asthma, chronic obstructive pulmonary disease (COPD) and allergic rhinitis. Studies with GSK123 via intravenous (IV), inhaled (IH) and intranasal (IN) routes in healthy volunteers and asthmatics have reported increases in heart rate (HR). Initial patient data suggest higher doses (>50mcg) of GSK123 would be required to provide clinical efficacy (FEV1 changes). A modelling strategy was utilised to address the tachycardia risk at higher doses of GSK123.
Objective: The objective of this analysis was to develop and validate a population PD model for GSK123 using data from studies in the Phase I program and to simulate a proposed study to quantify the risk of tachycardia at higher doses.
Methods: Model development and validation was performed using NONMEM V. 
There is an apparent hysteresis of 10-20 min between systemic plasma concentrations, C(t), and HR changes. Rather than model PK profiles via three administration routes including an effect compartment, concentrations were transformed using an approximate effect compartment
E(t) = C(t) (1 - exp(- KEO(T- Tdose)))
which introduces a lag time for times less than ~4/KEO. HR changes were fitted to an Emax model with variability in individual responses for H0 (baseline), Hmax, EC50, n (slope), KEO (hysteresis).
The model was initially fitted to the IV data (189 C(t)-HR points) and independently validated using a Bayesian prediction of the IN and IH data (506 points). Finally, the model was used to simulate a repeat dose inhaled study of varying doses of GSK123 using a PK model of IH administration in healthy volunteers. Outcome measure was an estimate of the probability that a patient will experience HR increases greater than some threshold for a given dose.
Results: The intravenous infusion data fitted a sigmoid Emax model with the effect of hysteresis modelled using an approximate lag function where KEO corresponds to lag of ~25 min after Tmax. The model was validated by predicting conc-heart rate response from inhaled and intranasal healthy volunteer (HV)studies - Model confirmed asthmatic patients to have similar HR response as HV's.
Results from the CTS also showed that the percentage of subjects predicted to experience at least one increase in HR above threshold during the trial (1, 2 or 14 doses) were as follows: 50% of subjects predicted to exceed 30 bpm increase at 75 mcg dose, rising to 75% of the subjects for 150 mcg. At a threshold of 40 bpm increase, 20% of subjects were predicted to exceed it at 75 mcg dose rising to 50% for 150 mcg dose. Results of the CTS were subsequently confirmed with actual patient data in COPD at one of the doses of GSK123 studied.
Conclusions: When corrected for hysteresis via an approximate lag time, HR changes were shown to be independent of administration route of GSK123 and disease status. The risk of tachycardia at proposed doses was shown to be unacceptable. The approximate effect compartment is a useful tool for rapidly generating PD models where hysteresis is evident via multiple administration routes.

Comparison between Gauss Hermite quadrature and NONMEM on the ability to detect subpopulations

A. Lemenuel-Diot(1), N.frey(2), C. Laveille(2), R. Jochemsen(2), A. Mallet(1)
(1)INSERM U436, Dept Biomathematics, CHU Pitie Salpetriere, 91 bd de l'Hôpital, 75013 Paris, France. (2)Institut de Recherches Internationales Servier, 6 place des Pléiades, 92415 Courbevoie Cedex, France
poster
Introduction and Objectives: The Gauss Hermite quadrature method allows to get an accurate approximation of the likelihood function by expressing the integral-based individual likelihood according to an adjustable and an easy way to compute expression: weighted values of the individual likelihood function calculated for tabulated nodes. In order to determine the advantage of an accurate approximation of the likelihood function, the Gauss Hermite quadrature method was compared to NONNEM for different features.The aim of the present work was to study the ability of Gauss Hermite quadrature and NONMEM for one specific feature : the detection of subpopulations.
Methods: Simulations/estimations were performed to compare Gauss Hermite quadrature method to NONMEM. Populations made up of two components were simulated with different distribution characteristics. The criteria of comparison between the two approaches were the power of detection of these two simulated subpopulations and the precision of estimations of the parameters. Since the two approaches do not use the same statistical test for the detection of the mixture model, it was necessary to adjust these tests before doing any comparison. The selection between two nested models (i.e. one component versus two components) is made using the log likelihood ratio test for NONMEM and the Kullback Leibler test for the Gauss Hermite quadrature method. A specific simulation/estimation approach was used to adjust each method in order to obtain different type I errors.
Results: With these two methods, the power of detection is quite linked to the characteristics of the mixture distributions : the differences between the mean of the components, their variances and the weights of the mixture. However, the ability to detect subpopulations is not the same for the two methods and these differences will be presented at the PAGE meeting.

Establishing a tool for individualised dosing of gabapentin - The use of a non-parametric population kinetics model in the MM-USCPACK software, a new tool for clinical dosage optimization.

Kristin Cecilie Carlsson(1), Heidi Hansen(1), Roger Jelliffe(2), Nils Ove Hoem(3).
(1)Dept. of Pharmacology, School of Pharmacy, University of Oslo, Norway.(2) Laboratory of Applied Pharmacokinetics, University of Southern California, USA. (3) Smerud Medical Research, Oslo Norway.
poster
To be able to use pharmacokinetic tools in clinical practice, they must be easily available to the physician at the clinic, or even bedside. To be clinically useful, even in many everyday situations, such tools must be able to handle relatively complex pharmacokinetic models, and also be able to take into account continuous changes in the patient's condition.
The MM-USCPACK software employs an interacting multiple-model (non-parametric) strategy for analyzing previous serum concentration-time data and predicting future dosage regimens. The MM-USCPACK software can be used on a portable computer and have a jump function that makes it possible to handle continuously changing parameter estimates. 
To facilitate individualized dosing of gabapentin, a population pharmacokinetic model has been developed consisting of an absorption and a central compartment, and with speed of elimination described as a linear function of creatinine clearance.
We have dose monitored a small number of patients who were treated with gabapentin against neuropathic pain (8 patients with a total of 19 dosage interval profiles). 
Serum concentration levels, analgesic effects and adverse effects measured by a visual analog scale, were registered as time variables. The covariates gender, age, height, weight, serum creatinine and total daily dose were registered as patient characteristics. 
The parameters for the pharmacokinetic model were first estimated by a parametric standard two-stage Bayesian population tool (IT2B) and then with the Non-Parametric Adaptive Grid (NPAG) tool recently developed by The Laboratory of Applied Pharmacokinetics. The resulting population pharmacokinetic model can together with the MM-USCPACK software be used to optimize dosing of gabapentin in the chosen patient population. 

Evaluation Of An Osteoporosis Biomarker Model For Simulation Using Posterior Predictive Check Technique

P. Girard, L. Claret, W. Ebling and S.T. Forgue, M. Heathman, A. Ghosh, C.T. Benson
Pharsight Corp, Mountain View CA and Eli Lilly & Co, Indianapolis IN.
poster

Purpose Osteocalcin (OC) is a biomarker of drug effect on osteoporosis progression. A decrease in OC has been shown to be correlated with a decrease in fractures risks in postmenopausal osteoporotic women. This makes this biomarker interesting for the purpose of clinical trial simulation in earlier phase development, when the length of trials does not allow observation of the clinical endpoint. A posterior predictive check (PPC) technique was used to qualify a model of OC as a prerequisite for trial simulation. 
Methods Data were combined across 1,456 postmenopausal women who received placebo (calcium or Ca+vitamin D) or the SERM raloxifene (30, 60 or 150 mg) in 4 parallel-group trials. Serum OC and covariates measured at 0 to 12 months were fitted to an integrated indirect response model: 
OC(t)= Ki/Ko (1- f(D) (1-e-Ko t )). 
Here, Ki and Ko are 0- and 1-order rate constants, and f(D)= EmaxD/(D50+D) if dose D>0 and f(D)=PL if D=0. Parameters and between-patient variability in Ki, Emax and PL were estimated with NONMEM. Observed OC values were compared to values simulated with a degenerate posterior distribution or a multivariate normal one, with means set to their point estimates and covariance matrix set to the precision matrix. 
Results The best model included effects of urinary type 1 collagen on input rate Ki and osteopenia status on maximal SERM effect Emax. Common goodness-of-fit plots suggested an excellent fit; however, both PPC techniques revealed misspecification that could potentially undermine trial simulations. The specific problem was corrected by constraining placebo to have a beneficial effect.
Conclusions PPC accounts for all sources of randomness and is a powerful technique to qualify any population pharmacodynamic model intended to support clinical trial simulation.

Comparison of different approaches for the analysis of drug exhibiting nonlinearity of Cmax to increasing doses

Xuejun Chen, Suresh Mallikaarjun, Steven L. Bramer
Otsuka Maryland Research Institute, 2440 Research Blvd., Rockville, MD 20850
poster
Purpose: The PK of compound X appeared to be nonlinear with Cmax increasing less than proportionally with increasing of dose. The goal of this study is to explore the approach to modeling drugs showing nonlinearity of Cmax to increasing doses.
Methods: 197 subjects dosed with 5-250 mg oral administration of compound X contributed to the 3775 data samples were analyzed. In order to model the less than proportional increase in plasma concentrations, several approaches were attempted: 1) absorption process consisting of first order of absorption and then zero-order of absorption after certain dose; 2) expressing ka as Michaelis-Menten function of dose; 3) determining the inflection point for nonlinearity. These methods were evaluated by examining the objective function and goodness of fit.
Results: The first two approaches provided physiological relevance to the pharmocokinetic interpretation of the nonlinear PK of compound X. However, the best model, splitting pharmacokinetic parameters by dose, provided best fit to the pooled data. 
Conclusions: For drugs exhibiting less than proportional increases in Cmax, splitting pharmacokinetic parameters based upon the inflection point provides an alternative approach.

Nonparametric population analysis of stavudine pharmacokinetic data in neonates, infants, children and adults

Y. Merlé (1,2), J.M. Tréluyer (2,3), E. Rey (3), J. Dimet (3), G. Leleu (4), S. Blanche (5).
(1) INSERM, France, (2) EA 1833, University René Descartes, Paris, France, (3) Department of Clinical Pharmacology, CHU Cochin-Saint Vincent de Paul, Paris, France, (4) Medical department of Infectiology-Immunology, BMS France, Rueil-Malmaison, France, (5) Department of paediatric immunohaematology. CHU Necker- Enfants malades, Paris, France.
poster
Objectives: The aims of our work were: i) to describe the reverse transcriptase inhibitor stavudine pharmacokinetics (PK) in populations of neonates, infants, children and adults; ii) to determine the extent to which various covariates account for PK interindividual variability; iii) to investigate the relationship between exposure and age and body weight.
Methods: Therapeutic drug monitoring data were retrospectively collected from 452 patients and analysed by the NPML1 method, six covariates being included in the analysis (age, body weight, sex, plasma creatinine, urea, and galenical form). We investigated the extent to which each covariate accounted for the variability of each PK parameter by computing the relative expected reduction of parameter variability due to each covariate2. The relationships (if any) between PK parameters and covariates were explored by a graphical method3. The area under the curve during 24 hours (AUC 24h) was calculated for each patient from the Bayesian individual parameters estimates. A nonparametric correlation analysis was then performed between AUC 24h and the age and weight.
Results: Our results illustrate the high interindividual variability of both apparent clearance (CL/F) and volume of distribution (V/F) (104 % and 42 % respectively). Age and weight were significant covariates for CL/F variability and age was a significant covariate for variability of V/F. Plasma creatinine was a significant covariate for variability of elimination constant rate and in patients with renal impairment. Despite the moderate increase in estimated AUC 24h, significant correlations were found between exposure and age or weight (p < 10-3).
Conclusion: Age, weight, and plasma creatinine were identified as covariates that explain variability in the pharmacokinetic parameters of stavudine in a heterogeneous population (neonates to elderlies). Stavudine exposure was related to age and weight.
References:
[1] Mallet A. A maximum likelihood estimation method for random coefficient regression models. Biometrika 1986; 73: 645-656.
[2] Tréluyer JM, Merlé Y, Semlali A, Pons G. Population pharmacokinetic analysis of netilmicin in neonates and infants with use of a nonparametric method. Clin Pharmacol Ther 2000; 67 (6): 600-9.
[3] Mentré F, Pousset F, Comets E, Plaud B, Diquet B, Montalescot G, et al. Population pharmacokinetic-pharmacodynamic analysis of fluindione in patients. Clin Pharmacol Ther 1998; 63 (1): 64-78.

Influence of high levels of alpha-1-acid glycoprotein in the pharmacokinetics and the analgesic effect of methadone in the rat: A population approach

Monica Rodriguez(1), Nerea Leal(1), Rosario Calvo(1), Elena Suarez(1), Ignacio Ortega(1), John C Lukas(2)
(1)Department of Pharmacology, School of Medicine, University of the Basque Country, Leioa, Vizcaya, Spain; (2)Department of Pharmacy, Laboratory of Pharmacokinetics and Biopharmaceutics, University of Athens, Greece
poster
Background: The pharmacokinetics (PK) and pharmacodynamics (PD) of methadone (M), an opiate agonist, shows still unclarified inter-individual variability [1]. M is highly bound to a1-acid glycoprotein (AGP). AGP is known to increase in several pathological situations (e.g. infection, inflammation), and may affect the PK/PD of several drugs dependent on and also independently of protein binding [2].
Purpose: To characterise the influence of high levels of AGP on methadone's analgesic effect and PK in the animal model.
Methods: AGP levels were increased by two different methods: (a) experimental inflammation with turpentine oil (inflammation is known to alter per se the PK of several drugs) [3] and (b) by directly infusing the protein. Tail-flick analgesia was measured after i.v. M injection (0.35 mg/kg), from 0 to 120 min, in control (n=20), turpentine pretreated (TP) (n=10), and AGP infused (AI) (n=16) male Sprague-Dawley rats. The PK were evaluated in separate control (n=20; m=23), TP (n=30; m=37) and AI (n=14; m=16) rats, after the same dose of M i.v.. The unbound fraction (fu) as well as AGP and albumin levels were measured. A bicompartmental model best described the PK using NONMEM. The objective function, SE estimates and residual plots were used for comparisons.
Results: The area under the effect-time curve was (mean ± SD) 978 ± 130 min in the AI group, 1789 ± 295 min in the TP group, both significantly lower than the 4871 ± 393 min in the control (p<0.0001). On the contrary, the concentration (Cp) vs time profiles were higher in TP and particularly AI (C0=1141.2 m g/L and 208.3 m g/L in AI and TP rats respectively vs 123.2 m g/L in controls) and therefore corresponded inversely to the effect vs time relative magnitudes. The FOCE PK parameters were, for the control central clearance (mean [interindividual CV%]) CL=0.024 L/min (19%), central volume Vc=0.68 L (31%), intercompartmental clearance Q=0.11 L/min (31%) and deep tissue volume Vt=0.93 L (31%). For TP, CL=0.016 L/min (19%), Vc=0.39 L (21%), Q=0.04 L/min (79%), Vt=0.58 L (31%). For AI, CL=0.006 L/min (50%), Vc=0.06 L (31%), Q=0.01 L/min (31%), Vt=0.07 L (no CV estimate). All differences were significant compared to the controls (p<0.005). Covariate modelling was hindered by the destructive sampling design [4]. For TP, Vc=0.69 - 0.23*AGP + 0.16*(AGP-1.7)2 (5%). The AGP levels were 0.4 g/L, 1.6 g/L and 6 g/L for control, TP and the AI, and the fu was 23%, 11% and 9% respectively. The PK parameters were not corrected by the fu.
Conclusions: Increased AGP levels relate to significant changes in the PK parameters and their population statistics. AGP appears responsible for these alterations, beyond protein binding (i.e. lack of correction by the fu). We are currently evaluating PD models to explain the lack of relationship between Cp and effect. The results could relate to man under conditions of infection, frequent in methadone treated patients.
References:
[1] Eap CB, Buclin T, Baumann P: Interindividual variability of the clinical pharmacokinetics of methadone: Implication for the treatment of opioid dependence. Clin Pharmacokinet 2002; 41:1153-93
[2] Fournier T, Medjoubi-N N, Porquet D: Alpha-1 acid glycoprotein. Biochimica et Biophysica Acta 2000; 1482: 157-71
[3] Jauregizar N, Calvo R, Suarez E, Quintana A, Raczka E, Lukas JC: Altered disposition and effect of lerisetron in rats with elevated alpha1-acid glycoprotein levels. Pharm Res 2001; 18:838-45
[4] Ette EI, Kelman AW, Howie CA, Whiting B: Analysis of animal pharmacokinetic data: performance of the one point per animal design. J Pharmacokin Biopharm 1995; 23:551-66