Likelihood Based Inference for Linear and Nonlinear Mixed-Effects Models with Censored Response Using the Multivariate-t Distribution

Mixed models are commonly used to represent longitudinal or repeated measures data. An additional complication arises when the response is censored, for example, due to limits of quantification of the assay used. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. Motivated by a concern of sensitivity to potential outliers or data with tails longerthan-normal, we aim to develop a likelihood based inference for linear and nonlinear mixed effects models with censored response (NLMEC/LMEC) based on the multivariate Student-t distribution, being a flexible alternative to the use of the corresponding normal distribution. We propose an ECM algorithm for computing the maximum likelihood estimates for NLMEC/LMEC with standard errors of the fixed effects and likelihood function as a by-product. This algorithm uses closed-form expressions at the E-step, which relies on formulas for the mean and variance of a truncated multivariate-t distribution, and can be computed using available software. The proposed algorithm is implemented in the R package tlmec. An appendix which includesfurther mathematical details, the R code, and datasets for examples and simulations are available as supplements. The newly developed procedures are illustrated with two case studies, involving the analysis of longitudinal HIV viral load in two recent AIDS studies. In addition, a simulation study is conducted to assess the performance of the proposed approach and its comparison with the approach by Vaida and Liu (2009).