The SAEM algorithm for group comparison tests in longitudinal data analysis based on non-linear mixed-effects model

Non-linear mixed-effects models (NLMEMs) are used to improve information gathering from longitudinal studies and are applied to treatment evaluation in disease-evolution studies, such as human immunodeficiency virus (HIV) infection. The estimation of parameters and the statistical tests are critical issues in NLMEMs since the likelihood and the Fisher information matrix have no closed form. An alternative method to numerical integrations, in which convergence is slow, and to methods based on linearization, in which asymptotic convergence has not been proved, is the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. For the Wald test and the likelihood ratio test, we propose estimating the Fisher information matrix by stochastic approximation and the likelihood by importance sampling. We evaluate these SAEM-based tests in a simulation study in the context of HIV viral load decrease after initiation of an antiretroviral treatment. The results from this simulation illustrate the theoretical convergence properties of SAEM. We also propose a method based on the SAEM algorithm to compute the minimum sample size required to perform a Wald test of a given power for a covariate effect in NLMEMs. Lastly, we illustrate these tests on the evaluation of the effect of ritonavir on the indinavir pharmacokinetics in HIV patients and compare the results with those obtained using the adaptative Gaussian quadrature method implemented in the SAS procedure NLMIXED.