A bi-dimensional finite mixture model for longitudinal data subject to dropout

In longitudinal studies, subjects may be lost to follow-up and, thus, present incomplete response sequences. When the mechanism underlying the dropout is nonignorable, we need to account for dependence between the longitudinal and the dropout process. We propose to model such a dependence through discrete latent eects, which are outcome-specific and account for heterogeneity in the univariate profiles. Dependence between prolfies is introduced by using a probability matrix to describe the corresponding joint distribution. In this way, we separately model dependence within each outcome and dependence between outcomes. The major feature of this proposal, when compared to standard finite mixture models, is that it allows the nonignorable dropout model to properly nest its ignorable counterpart. We also discuss the use of an index of (local) sensitivity to nonignorability to investigate the effects that assumptions about ignorability of the dropout process may have on model parameter estimates. The proposal is illustrated via the analysis of data from a longitudinal study on the dynamics of cognitive functioning in the elderly.