Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.262542566Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq-Brazil)Fundacao de Amparo a Pesquisa do Estado de Sao Paulo from FAPESP-Brazil [2013/21468-0, 2014/02938-9]Grant FONDECYT from the Chilean government [1130233]FAPESP-Brazil [2012/19445-0, 2014/11831-3]Polish National Center for Science [UMO-2013/10/M/ST1/00096]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)