We generalize Lyles et al.’s (2000) random regression models for longitudinal data, accounting for both undetectable values and informative drop-outs in the distribution assumptions. Our models are constructed on the generalized multivariate theory which is based on the Elliptically Contoured Distribution (ECD). The estimation of the fixed parameters in the random regression models are invariant under the normal or the ECD assumptions. For the Human Immunodeficiency Virus Epidemiology Research Study data, ECD models fit the data better than classical normal models according to the Akaike (1974) Information Criterion. We also note that both univariate distributions of the random intercept and random slope and their joint distribution are non-normal short-tailed ECDs, and that the error term is distributed as a non-normal long-tailed ECD if we don’t use the low undetectable limit or half of it to replace the undetectable values. Instead, we use the ECD cumulative distribution function to calculate the contribution to the likelihood due to the undetectable values.