## Preprint 2016-10

## Luis M. Castro, Víctor H. Lachos, Tsung-i Lin, Larissa A. Matos:

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

### Abstract:

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 complication arises when these continuous repeated measures have a heavy-tailed behaviour. For such data structures, we propose a robust nonlinear censored regression model based on the scale mixtures of normal (SMN) distributions. To take into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. A stochastic approximation of the EM (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 as a by-product. The practical utility of the proposed method is exemplified using both simulated and real data.