  Latent Markov (LM) models represent an important tool of analysis of
longitudinal data when response variables are affected by time-varying
unobserved heterogeneity, which is accounted for by a hidden Markov chain. In
order to avoid bias when using a model of this type in the presence of
informative drop-out, we propose an event-history (EH) extension of the LM
approach that may be used with multivariate longitudinal data, in which one or
more outcomes of a different nature are observed at each time occasion. The EH
component of the resulting model is referred to the interval-censored drop-out,
and bias in LM modeling is avoided by correlated random effects, included in
the different model components, which follow a common Markov chain. In order to
perform maximum likelihood estimation of the proposed model by the
Expectation-Maximization algorithm, we extend the usual backward-forward
recursions of Baum and Welch. The algorithm has the same complexity of the one
adopted in cases of non-informative drop-out. Standard errors for the parameter
estimates are derived by using the Oakes' identity. We illustrate the proposed
approach through an application based on data coming from a medical study about
primary biliary cirrhosis in which there are two outcomes of interest, the
first of which is continuous and the second is binary.
