Heavy-tailed longitudinal regression models for censored data: A likelihood based perspective

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Moreover,it is quite common to observe viral load measurements collected irregularly over time. A complica-tion arises when these continuous repeated measures have a heavy-tailed behaviour. For such data structures, we propose a robust censored linear model based on the scale mixtures of normal distributions (SMN family). To take into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. A stochastic approximation of the EM algorithm (SAEM algorithm) is developed to obtain the maximum likelihood estimates of the model parameters. The main advantage of this new procedure allows us to estimate the parameters of interest and evaluate the log-likelihood function in an easy and fast way. Furthermore, the standard errors of the fixed effects and predictions of unobservable values of the response can be obtained asa by-product. The practical utility of the proposed methodology is exemplified using both simulatedand real data.