This article shows an example of longitudinal analysis of incomplete data where the response variable can be left-censored (because of the assay detection threshold) and where measurements may be missing because of informative drop-outs. This is illustrated by the change in plasma viral load of patients infected with human immunodeficiency virus (HIV) after the initiation of antiretroviral treatment. Clinical events such as opportunistic diseases and death may occur leading to an informative censoring of data. A parametric random-effects based selection model is presented. A direct likelihood maximisation allows to take into account left-censoring of plasma viral load. Mixture models are proposed to test the gaussian distribution assumption of left-censored data. The application shows the effect of taking into account left-censoring. Finally, handling for the left-censoring of response variables is easily feasible and allow to reduce biases. Dealing with informative drop-out is difficult because of the definition of the drop-out process, the choice of the model and the estimation of model parameters. However, it is most often necessary, at least as a robustness analysis, because it may have a huge effect on results.