A semiparametric mixed-effects model for censored longitudinal data

In longitudinal studies involving laboratory-based outcomes, repeated measurements can be censored due to assay detection limits. Linear mixed-effects (LMEs) models are a powerful tool to model the relationship between a response variable and covariates in longitudinal studies. However, the linear parametric form of linear mixed-effect models is often too restrictive to characterize the complex relationship between a response variable and covariates. More general and robust modeling tools, such as nonparametric and semiparametric regression models, have become increasingly popular in the last decade. In this article, we use semiparametric mixed models to analyze censored longitudinal data with irregularly observed repeated measures. The proposed model extends the censored linear mixed-effect model and provides more flexible modeling schemes by allowing the time effect to vary nonparametrically over time. We develop an Expectation-Maximization (EM) algorithm for maximum penalized likelihood estimation of model parameters and the nonparametric component. Further, as a byproduct of the EM algorithm, the smoothing parameter is estimated using a modified linear mixed-effects model, which is faster than alternative methods such as the restricted maximum likelihood approach. Finally, the performance of the proposed approaches is evaluated through extensive simulation studies as well as applications to data sets from acquired immune deficiency syndrome studies.