Censored Linear Regression Models for Irregularly Observed Longitudinal Data using the Multivariate-t Distribution

In AIDS studies it is quite common to observe viral load measurements collected irregularlyover time. Moreover, these measurements can be subjected to some upper and/or lower detection limitsdepending on the quantification assays. A complication arises when these continuous repeated measureshave a heavy-tailed behavior. For such data structures, we propose a robust structure for a censoredlinear model based on the multivariate Student-t distribution. To compensate for the autocorrelationexisting among irregularly observed measures, a damped exponential correlation structure is employed.An efficient EM-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-t distribution. The methodology is illustrated through an application to an HIV-AIDS study and several simulation studies.