Malte Selch Larsen (1,2), Rasmus Vestergaard Juul (3), Mads Kreilgaard (1), Annemarie T. Kristensen (2) and Ulrika S. H. Simonsson (4)
(1) Haemophilia PK & ADME, Haemophilia Research, Global Research, Novo Nordisk A/S, Maaloev, Denmark; (2) Department of Veterinary Clinical Sciences, University of Copenhagen, Frederiksberg, Denmark; (3) Quantitative Clinical Pharmacology, Novo Nordisk A/S, Soeborg, Denmark; (4) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives
Historically, clinical trials of haemophilia with inhibitors have been challenged by i) the small patient population, ii) event-type outcome and iii) potential placebo effect [1]. There is therefore a need to optimize the clinical trial designs and analysis methods in this therapeutic area.
The aim of this work was to evaluate the impact of different trial designs and study conditions on the estimated drug potency and to compare traditional statistical methods with repeated time-to-event (RTTE) modelling in terms of power of finding a statistical significant drug effect.
Methods
Baseline analysis of bleeding events
Baseline data on the occurrence of bleeding events (BE) in 23 haemophilia patients with inhibitors were obtained from a study by Ljung et al [2]. A RTTE model was developed to describe the probability of BE over time in haemophilia patients with inhibitors. Model selection was based on comparison of the objective function value, Kaplan-Meier visual predictive checks and precision of parameter estimates. The Laplace estimation method in NONMEM version 7.3 [3] was used.
Simulation model, trial designs and study conditions
The hypothetical drug (drugH) was assumed to be given subcutaneously once a week and to display a two-compartment pharmacokinetic (PK) distribution with first-order absorption. The exposure-response relationship of drugH was described by an Emax model and a proportional placebo effect of 25 % [1] was implemented for the treatment period.
Four different trial designs, previously used in clinical trials of haemophilia [2, 4, 5], were evaluated: parallel-group design (PG-design), placebo-controlled parallel-group design (PGPLC-design), crossover design (XO-design) and placebo-controlled crossover design (XOPLC-design). Study conditions evaluated in this work included different sample sizes, study durations and doses.
Evaluation of precision and accuracy of the estimated drug potency
The stochastic simulation and estimation (SSE) method in PsN [6, 7] was used to evaluate the effect of different trial designs and study conditions on the precision and accuracy of the estimated EC50 of drugH (1000 samples). The accuracy was evaluated based on the median, while precision was evaluated based on the width of the 95% confidence interval and the percentage of estimates with relative error ± 75%.
To illustrate the effect of an inaccurate estimate of EC50 on dose selection, the relationship between annualized bleeding rate (ABR) and dose of drugH were plotted for the true EC50 value and for EC50 estimates with ± 50 and 75% relative error, respectively. Assuming a treatment aim of 3 BE/year, the appropriate dose was derived for each EC50 estimate and the resulting ABR was compared to the treatment target.
Evaluation of power
The SSE method was used to estimate the relationship between sample size and the power to identify a significant treatment effect for RTTE modelling, t-test (two-sided) and negative binomial regression (p=0.05).
Results
The baseline hazard was accurately described by an exponential distribution with a hazard constant of 22.6 year-1 and inter-individual variability of 77.3% coefficient of variation. All trial designs and study conditions provided accurate estimates of EC50. However, the crossover designs displayed up to four-fold higher precision relative to the parallel-group trial. In general, the presence of a placebo-group did not increase the precision. However, a beneficial effect of the placebo-group was observed for the lower dose, probably reflecting the increased difficulty of separating the drug effect from the placebo effect when the drug effect is low.
To meet the assumed treatment target of 3 BE/year, a dose of 150 mg/kg would have been required given the true EC50. In case of inaccurate estimates of EC50 e.g., relative error of -50 and -75%, doses of 75 and 37.5 mg/kg would have been selected resulting in ABRs of approximately 5 and 9 BE/year, respectively.
The crossover designs displayed up to three-fold higher power relative to the parallel-group designs. As for the traditional statistical methods, the t-test and negative binomial regression systemically displayed a lower power than RTTE modelling.
Conclusions
We found that utilization of crossover designs in combination with RTTE modelling can markedly reduce the required sample size and study duration, while ensuring high power and precise estimation of EC50, in clinical trials of haemophilia with inhibitors.
References
[1] Lusher JM, Shapiro SS, Palascak JE, Rao AV, Levine PH, Blatt PM, Group tHS. Efficacy of Prothrombin-Complex Concentrates in Hemophiliacs with Antibodies to Factor VIII. N Engl J Med. 1980; 303: 421-5.
[2] Ljung R, Karim FA, Saxena K, Suzuki T, Arkhammar P, Rosholm A, Giangrande P, The Pioneer™ I. 40K glycoPEGylated, recombinant FVIIa: 3-month, double-blind, randomized trial of safety, pharmacokinetics and preliminary efficacy in hemophilia patients with inhibitors. J Thromb Haemost. 2013; 11: 1260-8.
[3] Beal SL, Sheiner LB, Boeckmann A, Bauer R. NONMEM Users Guides. (1989-2009) ICON Development Solutions. Ellicott City, MD, USA, 2009.
[4] ClinicalTrials.gov. Trial Investigating Safety, Pharmacokinetics and Pharmacodynamics of Concizumab Administered Subcutaneously to Haemophilia A Subjects. 2015
[5] ClinicalTrials.gov. Study Comparing On-Demand Treatment With Two Prophylaxis Regimens Of BeneFIX In Patients With Severe Hemophilia B. 2006.
[6] Keizer RJ, Karlsson MO, Hooker A. Modeling and Simulation Workbench for NONMEM: Tutorial on Pirana, PsN, and Xpose. CPT Pharmacometrics Syst Pharmacol. 2013; 2: 1-9.
[7] https://uupharmacometrics.github.io/PsN/ (accessed 18/02/21).
Reference: PAGE 27 (2018) Abstr 8486 [www.page-meeting.org/?abstract=8486]
Poster: Drug/Disease Modelling - Other Topics