Extending multivariate Student's- t $$ t $$ semiparametric mixed models for longitudinal data with censored responses and heavy tails

Abstract

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's $t$ -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Keywords: EM algorithm; HIV viral load; Student's- t $$ t $$ distribution; censored data; mixed-effects model; semiparametric model.