Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model

The reduction of viral load is frequently used as a primary endpoint in HIV clinical trials. Nonlinear mixed-effects models are thus proposed to model this decrease of the viral load after initiation of treatment and to evaluate the intra- and inter-patient variability. However, left censoring due to quantification limits in the viral load measurement is an additional challenge in the analysis of longitudinal HIV data. An extension of the stochastic approximation expectation-maximization (SAEM) algorithm is proposed to estimate parameters of these models. This algorithm includes the simulation of the left-censored data in a right-truncated Gaussian distribution. Simulation results show that the proposed estimates are less biased than the usual naive methods of handling such data: omission of all censored data points, or imputation of half the quantification limit to the first point below the limit and omission of the following points. The viral load measurements obtained in the TRIANON-ANRS81 clinical trial are analyzed with this method and a significant difference is found between the two treatment groups of this trial.