Some Alternatives to Likelihood ratio and Wald Tests for Pharmacogenetic studies using nonlinear mixed effect models.
Julie Bertrand (1), Emmanuelle Comets (1), Marylore Chenel (2) and France Mentré (1)
(1) UMR 738, INSERM, Université Paris Diderot, Paris, France; (2) Institut de Recherches Internationales Servier, Courbevoie, France
Objectives: Pharmacogenetics can help guiding the dose regimen, however due to the specificity of the genetic covariate methodological improvements are required. Indeed, the Wald and the likelihood ratio tests which are often used to detect a gene effect on a pharmacokinetic parameter using nonlinear mixed effect models (NLMEM) show inflated type I error on small sample size and/or with unevenly distributed genotypes [1, 2]. In this context, we develop and evaluate two alternatives: a permutation test for both statistics and the use of a F-distribution for the Wald test only.
Methods: In the second alternative, four different values are considered for the denominator degrees of freedom (df) i) a denominator df derived from balanced, multilevel one-way analysis of variance (DFPB), ii) a df proposed for NLMEM by Wolfinger (2000), iii) a df adapted for NLMEM from a method developed by Gallant (1975) in multivariate nonlinear models (DFG) and iv) an extension to NLMEM of the Satterthwaite df formula (DFFC).
All methods are evaluated in terms of type I error and power based on a simulation study as described in [1, 2]. The influence of the estimation algorithm is explored using both FOCE-I in NONMEM 7 and SAEM in MONOLIX 2.1. Also, all methods are applied to the analysis of the pharmacogenetics of indinavir in 40 HIV patients recruited in the COPHAR2-ANRS 111 trial [3].
Results: Using the permutation test, the type I error estimates of the Wald test and the LRT are non-significantly different from the nominal level of 5%, with both algorithms whereas the only method based on an F-distribution that corrects for the type I error inflation of the Wald test is the DFG method with SAEM. Using the simulation-based correction or the permutation test, the corrected power estimates for the Wald test are much lower using FOCE-I (18.6 and 27.4%) than SAEM (71 and 73%).
In the final model built for the real data, the CYP 3A4*1B polymorphism remains associated to the indinavir absorption rate constant whereas the effect of age is discarded based on the p-value estimates from the permutation test and the DFG approach. The CYP 3A4*1B polymorphism was also significantly associated with lower indinavir maximal concentration and decreased short term triglycerids toxicity.
Conclusions: As permutation comes with a substantial computational burden, it should be considered only when decisions based respectively on the asymptotic test and the Gallant alternative are discordant.
References:
[1] Bertrand, J., Comets, E., and Mentré, F. (2008). Comparison of model-based tests and selection strategies to detect genetic polymorphisms influencing pharmacokinetic parameters. Journal of Biopharmaceutical Statistics 18, 1084-1102.
[2] Bertrand, J., Comets, E., Laffont, C., Chenel, M., and Mentré, F. (2009). Pharmacogenetics and population pharmacokinetics: impact of the design on three tests using the SAEM algorithm. Journal of Pharmacokinetics and Pharmacodynamics 36, 317-339.
[3] Bertrand, J., Tréluyer, J., Panhard, X., Tran, A., Rey, E., Salmon-Céron, D., Duval, X., Mentré, F., and the COPHAR2-ANRS 111 study group. (2009a). Influence of pharmacogenetics on indinavir disposition and short-term response in HIV patients initiating HAART. European Journal of Clinical Pharmacology 65, 667-678.
