Extension of the SAEM algorithm for nonlinear mixed models with two levels of random effects

TL;DR

This paper extends the SAEM algorithm to estimate parameters in complex multi-level nonlinear mixed effects models with two random effects levels, demonstrating improved accuracy over existing methods in pharmacokinetic data analysis.

Contribution

The paper introduces an extended SAEM algorithm tailored for two-level random effects in nonlinear mixed models, enhancing parameter estimation accuracy.

Findings

Extended SAEM outperforms FOCE in bias and RMSE on simulated data.

Application to pharmacokinetic data reveals significant drug interaction effects.

Method effectively decomposes variability at multiple hierarchical levels.

Abstract

This article focuses on parameter estimation of multi-levels nonlinear mixed effects models (MNLMEMs). These models are used to analyze data presenting multiple hierarchical levels of grouping (cluster data, clinical trials with several observation periods,...). The variability of the individual parameters of the regression function is thus decomposed as a between-sub ject variability and higher levels of variability (for example within-sub ject variability). We propose maximum likelihood estimates of parameters of those MNLMEMs with two levels of random effects, using an extension of the SAEM-MCMC algorithm. The extended SAEM algorithm is split into an explicit direct EM algorithm and a stochastic EM part. Compared to the original algorithm, additional sufficient statistics have to be approximated by relying on the conditional distribution of the second level of random effects. This estimation method is evaluated on pharmacokinetic cross-over simulated trials, mimicking theophyllin concentration data. Results obtained on those datasets with either the SAEM algorithm or the FOCE algorithm (implemented in the nlme function of R software) are compared: biases and RMSEs of almost all the SAEM estimates are smaller than the FOCE ones. Finally, we apply the extended SAEM algorithm to analyze the pharmacokinetic interaction of tenofovir on atazanavir, a novel protease inhibitor, from the ANRS 107-Puzzle 2 study. A significant decrease of the area under the curve of atazanavir is found in patients receiving both treatments.