  Dropout represents a typical issue to be addressed when dealing with
longitudinal studies. If the mechanism leading to missing information is
non-ignorable, inference based on the observed data only may be severely
biased. A frequent strategy to obtain reliable parameter estimates is based on
the use of individual-specific random coefficients that help capture sources of
unobserved heterogeneity and, at the same time, define a reasonable structure
of dependence between the longitudinal and the missing data process. We refer
to elements in this class as random coefficient based dropout models (RCBDMs).
We propose a dynamic, semi-parametric, version of the standard RCBDM to deal
with discrete time to event. Time-varying random coefficients that evolve over
time according to a non-homogeneous hidden Markov chain are considered to model
dependence between longitudinal responses recorded from the same subject. A
separate set of random coefficients is considered to model dependence between
missing data indicators. Last, the joint distribution of the random
coefficients in the two equations helps describe the dependence between the two
processes. To ensure model flexibility and avoid unverifiable assumptions, we
leave the joint distribution of the random coefficients unspecified and
estimate it via nonparametric maximum likelihood. The proposal is applied to
data from the Leiden 85+ study on the evolution of cognitive functioning in the
elderly.
