**Properties of different tests to detect the effect of a genetic covariate on pharmacokinetic parameters using the SAEM algorithm for several designs**

Julie Bertrand, Emmanuelle Comets, France Mentré

INSERM, U738; Université Paris 7, Paris, France

**Objectives:** To compare through a simulation study the statistical properties of three different tests used for selection of a genetic covariate for analyses with nonlinear mixed effects models. Different designs are studied in order to address the cases of asymptotic conditions (high number of subjects) or of sparse data.

**Methods:** We use the stochastic EM algorithm (SAEM) implemented in MONOLIX 2.1 [1] in the assessment of three methods to test for a gene effect: i) an ANOVA to test the difference between the empirical Bayes estimates of the fixed effects parameters among the genetic groups,_{ }ii) a global Wald test to assess whether fixed effects estimates for the genetic effect are significant, and iii) a likelihood ratio test (LRT) between models with and without the genetic covariate.

The simulation setting is inspired from a real case study [2]. We consider a one compartment model at steady-state with first order absorption and elimination and a genetic effect on the drug bioavailability through the parameter V/F.

We investigate several designs (N=number of subjects, n=number of samples/subject): i) N=40/n=4 similar to the original study, ii) N=80/n=2 sorted in 4 groups, optimized using PFIM software [3] which reflects sparse conditions, iii) a mixed design: N=20/n=4 plus N=80/n=1 that are only trough concentrations, and iv) N=200/n=4 to reach asymptotic conditions. The first three designs (all leading to a total of 160 observations) are simulated 1000 times under both the null and the alternative hypotheses to assess the type I error and the power of the three methods. We compute the shrinkage as well as the empirical relative standard errors (RSE) and consider the information criterion and the RSE predicted by PFIM.

**Results:** ANOVA has a correct type I error estimate across designs. Wald test and LRT show a slight but significant inflation of the type I error on the original design (small number of patients) and the mixed design (high shrinkage). This increase is corrected under asymptotic conditions (N=200/n=4). For each design, the corrected power is analogous for the three tests. Among the three designs with a total of 160 observations, the design N=80/n=2 provided both the best power and the lowest RSE on V/F.

**Conclusions:** This work underlines that inference on genetic effect does not necessarily require a conventional design with extensive sampling. Further studies are required to provide recommendations on which test to use according to the design.

**References:**

[1] Lavielle, M. *MONOLIX (MOdèles NOn LInéaires à effets miXtes)*, Orsay, MONOLIX Group (2005). www.monolix.org.

[2] Mentré, F. et al. Prospective trial to evaluate how therapeutic drug monitoring of protease inhibitors increases virologic success and tolerance of HAART (COPHAR2 - ANRS 111 trial). *12th Conference on Retroviruses and Opportunistic Infections* Boston, USA (2005).

[3] Retout, S., Mentré, F. Optimisation of individual and population designs using Splus. *J. Pharmacokinet. Pharmacodyn.* 30, 417-443 (2003). www.pfim.biostat.fr.

During this work, Julie Bertrand was supported by a grant from Servier Research Group, France.