Pharmacokinetic comparability between two populations using nonlinear mixed effect models: a Monte Carlo study

Abstract

'Are two populations the same or are they different' is a question that is often faced in clinical pharmacology trials e.g., a pharmacokinetic trial studying a particular drug in racially different groups. To address this question, concentration-time data were simulated from a reference and test population, where in the latter the clearance, sample size, and sampling design were systematically varied. It was of interest to determine whether the estimates of clearance from the two groups were the same or different. Two approaches were used to estimate the empirical Bayes estimates (EBEs) for clearance. One approach developed a population pharmacokinetic model for the reference population and the EBEs for the reference population were estimated from this model. The parameters of the reference population were fixed to their maximum likelihood estimates. The model was then applied to the test population dataset to estimate the EBEs of the test population using the MAXEVAL = 0 option in NONMEM. A second approach, the theta approach, combined the reference and test datasets into a single dataset and used population as a covariate in the model; the EBEs were estimated from this combined model. The power and type I error rate of each approach were calculated for each treatment combination using a variety of statistical tests to determine whether there was a difference in the distribution of the EBEs in the reference population compared to the test population. Our results suggest that either MAXEVAL or theta approaches can be used with informative sampling designs. In addition to reasonable power and type I error, both approaches gave almost identical results under a dense sampling design. To statistically compare the distribution of EBEs of pharmacokinetic parameters from a reference group to that of a test group, a T-test and DTS eCDF test are equally useful.

Keywords: Bayesian estimation; Kolmogorov–Smirnov; NONMEM; Nonlinear mixed effect models.