  Longitudinal data are characterized by the dependence between observations
coming from the same individual. In a regression perspective, such a dependence
can be usefully ascribed to unobserved features (covariates) specific to each
individual. On these grounds, random parameter models with time-constant or
time-varying structure are well established in the generalized linear model
context. In the quantile regression framework, specifications based on random
parameters have only recently known a flowering interest. We start from the
recent proposal by Farcomeni (2012) on longitudinal quantile hidden Markov
models, and extend it to handle potentially informative missing data mechanism.
In particular, we focus on monotone missingness which may lead to selection
bias and, therefore, to unreliable inferences on model parameters. We detail
the proposed approach by re-analyzing a well known dataset on the dynamics of
CD4 cell counts in HIV seroconverters and by means of a simulation study.
