Ben Francis
University of Liverpool
Objectives: The list of drugs which exist in healthcare to treat various conditions and diseases is vast with new drugs added every year. Many drugs cause adverse events which are dose dependent, consequently there is a need to identify the correct dose for each specific patient, which minimises their risk of having an adverse drugs reaction, whilst at the same time maximising the efficacy of the drug. The benefits of personalised medicine include more optimal treatment for the patient and the potential reduction in treatment costs from minimising the occurrence of adverse events [1]. However, the objective of a drug dose algorithm, finding the optimum dose, is complicated by the inter-individual variability in the response of each individual patient to a specific drug [2].
Population pharmacokinetics are often established in either drug trials or by similar research undertaken on drugs already in use. Population pharmacokinetic parameters are indicative of population dosing which will derive optimum dosage regimens for the average patient. Although, with large amounts of variability between patients, population dosing would be sub-optimal to provide therapeutic effect for most patients [3]. Post population analysis is required to classify and account for all the sources of variability in drug dose response. Thus enabling greater individualisation of drug therapy for patients and providing informed doses which aim to induce therapeutic plasma concentration levels as quickly as possible.
Using stochastic control methods, which utilize information on pharmacokinetic parameters and allow feedback of plasma concentration values from samples, creates an interactive drug dosing algorithm. The drug dose algorithm is also adaptive as factors which affect pharmacokinetic parameters can be inputted at anytime to update drug dosage regimens. This is particularly useful as the algorithm can derive dosage regimens based on probabilities of multiple models [4] whilst waiting for factors which require processing time, such as, pharmacogenetic information.
An example using the drug imatinib is provided, which is used to treat chronic myelogenous leukaemia. Imatinib is often administered as a 400mg dose regardless of patient dosing needs with 800mg doses prescribed if there is an apparent resistance to the drug [5]. In this example, seven day dosage regimens will be derived for twelve patients to demonstrate the effectiveness of the algorithm – the ability of the dosage regimen to guide the patient’s plasma concentration levels to maintain a therapeutic trough level of 1000ng/ml [6, 7]. Further, the ability of the drug dose algorithm to respond to varying degrees of non-compliance will be tested.
Methods: The drug dose algorithm is developed from stochastic control methods utilising data from a population pharmacokinetic model to make drug response estimates which can then be compared against noisy measurements (e.g. plasma concentration samples) of the response from each specific patient [8]. Using noisy measurements to update the analysis allows the system to become interactive; ultimately seeking to reduce the overall uncertainty of prediction and providing dose estimates which are tailored to the patient’s requirements. The pharmacokinetic system must first be presented as a stochastic control problem this involves determination of possible treatments, desired therapeutic outcome, time scale of treatment and expected responses from the system.
The pharmacokinetic compartmental model can be expressed as a set of differential equations or analytical solutions [9]. A stochastic component is then added to model to model small fluctuations that occur in patient’s plasma concentrations not explained by sources of variability. Traditionally the Weiner process has been added to an ordinary differential equation to show fluctuation in plasma concentration level [10]. However recently an alternative method has been proposed by Delattre et al. (2011) [11] where parameters are constantly perturbed around their mean value by the Weiner process thus leading to a variable gradient of the plasma concentration level. The later method is applied in the Imatinib case study. We simulated patient non-adherence to their prescribed drug dose regimen and then determined how well the drug dose algorithm responded with ‘days to return to therapeutic trough level’ as the primary outcome.
Results: In the Imatinib case study, firstly forecasting the plasma concentration of a patient taking the prescribed dose showed that patient trough levels were between 2.1 and 48.9% away from the therapeutic trough level. Dosage regimens derived by the drug dose algorithm advised alterations in ten out of the twelve patients included in the study. Dose adjustments in all but one patient (advised an average daily dose reduction of 129mg) advised an increase in their prescribed dosing, with average daily dose increases between 114 and 400mg. In simulation, the new dosage regimens kept patient trough levels between 0-5.4% away from the required therapeutic trough level of 1000ng/ml. Running the algorithm through compliance situations showed that ‘recuperation dosage regimens’ were derived which would restore the patient’s tough level to the required therapeutic trough level.
Conclusions: There is an important need for individualised dosing regimens that maximise efficacy of the drug, whilst at the same time minimising the risk of adverse drug reactions. The results from this case study show that patients who continue on the standard dosing protocol, in all but two cases, will fail to achieve a therapeutic trough level; whereas, stochastic control methods have been shown to estimate a dosing regimen which will induce a therapeutic trough level. This methodology can be applied to almost any drug with an established compartmental pharmacokinetic model. Additionally various clinical targets, other than therapeutic trough level, can be given to the drug dose algorithm. These include therapeutic concentration windows, concentration maximum targets and area under the curve targets. The main intention of this research is to compliment the clinician decision making process, therefore, further work will be undertaken to provide clinicians with percentage risks of therapeutic effect and adverse event. This further work will allow the clinician to make decisions based on information patient demographics, co-morbidity, co-medication, treatment risk factor and the drug dose algorithm output further combining clinical judgement with statistical models.
References:
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[8] Ozbek L, Efe M. An Adaptive Extended Kalman Filter with Application to Compartment Models. Communications in Statistics – Simulation and Computation 2004; 33: 145-158.
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[10] Bayard DS, Milman MH, Schumitzky A. Design of dosage regimens: A multiple model stochastic control approach. International Journal of Bio-Medical Computing 1994; 36: 103-115.
[11] Delattre M, Lavielle M. Pharmacokinetics and stochastic differential equations : model and methodology. In Pharmacokinetics and stochastic differential equations : model and methodology. PAGE:Venice, 2011.
Reference: PAGE 21 (2012) Abstr 2315 [www.page-meeting.org/?abstract=2315]
Poster: Other Modelling Applications