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Objectives: Genetic factors constitute part of the interindividual variability in pharmacokinetics (PK). The impact of genetic polymorphisms on PK is often analyzed using a non-compartmental approach but this requires extensive PK sampling and brings limited information, whereas modeling approaches provide deeper insight in the PK and the underlying processes. In this work, we evaluate the statistical properties of strategies using non-linear mixed effects models to detect the existence of a gene effect from PK data.

Methods: We evaluate, in a simulation study, the methods to test the influence of one single nucleotide polymorphism (SNP) on the PK of a drug  or, more specifically, to assess whether a given PK parameter has different mean values for different genotypes. To do so, we compare three methods and tests. First, we estimate the empirical Bayes estimates (EBE) in a model with no genetic covariate, and we test the existence of a relationship between the EBE of the individual parameters and the genetic covariate using an ANOVA. Second, we compare the nested models with and without a covariate for the SNP effect via a likelihood ratio test. Third, from the model where the genetic covariate is included, we use Wald tests to assess if the covariate effects are significantly different from 1. We study the impact of the estimation method by comparing the FO and FOCE algorithms in NONMEM and the SAEM [1] algorithm in MONOLIX.
The design of the simulation study is based on the sub-study of the PK of indinavir in patients in the  COPHAR 2-ANRS 111 clinical trial and included 40 patients with 4 PK samples each at steady state. In the study, all patients were genotyped for the C3435T and G12677A/T polymorphisms of the MDR-1 coding for P-glycoprotein. The PK is described using a one-compartment model with first order absorption and elimination. We simulate 1000 datasets with no gene effect (H0) and 1000 datasets assuming that the bioavailability was influenced by two exons (H1). Plausible effects of genetic polymorphism are derived from the literature and used for the simulations [2]. The distribution of the genetic covariate in the simulated datasets mimics the distribution of the two MDR-1 polymorphisms in the general population. For each method and the corresponding test, we evaluate the type I error and the power.

Results: The lack of precision of the FO algorithm results in a very important estimation bias leading to a very high increase of the type I error. FOCE and SAEM obtain similar results except for the method using Wald tests, where poor estimates of the standard errors led to low power for FOCE. However we met numerical difficulties in using FOCE on a number of data sets while SAEM provided estimates for all sets. The tests based on the EBE are the only one to keep an empirical type I error close to the expected 5%, whereas, for this design, the tests based on the LRT and the Wald statistics show a slight increase of the type I error under H0 which lead us to use the empirical threshold under H0 to correct the p-value of the test under H1. The corrected power was consistent for FOCE and SAEM.

Conclusions: Population methods can be used for gene effect detection and applied to data sets with sparse PK designs. In this study, a small inflation of the type I error was observed  for the LRT or Wald tests, but not with an ANOVA on the EBE. The SAEM algorithm had no convergence problems and no estimation bias and is therefore a powerful algorithm.

References:
[1] Kuhn and Lavielle. Maximum likelihood estimation in nonlinear mixed effects model, Computational Statistics and Data Analysis, 49 (2005), 1020-1038.
[2] Marzolini, Paus, Buclin, and Kim. Polymorphisms in Human MDR1 (P-glycoprotein): Recent advances and clinical relevance. Clinical Pharmacology and Therapeutics, 75 (2003), 13-33.