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Dropout represents a typical issue to be addressed when dealing withlongitudinal studies. If the mechanism leading to missing information isnon-ignorable, inference based on the observed data only may be severelybiased. A frequent strategy to obtain reliable parameter estimates is based onthe use of individual-specific random coefficients that help capture sources ofunobserved heterogeneity and, at the same time, define a reasonable structureof dependence between the longitudinal and the missing data process. We referto elements in this class as random coefficient based dropout models (RCBDMs).We propose a dynamic, semi-parametric, version of the standard RCBDM to dealwith discrete time to event. Time-varying random coefficients that evolve overtime according to a non-homogeneous hidden Markov chain are considered to modeldependence between longitudinal responses recorded from the same subject. Aseparate set of random coefficients is considered to model dependence betweenmissing data indicators. Last, the joint distribution of the randomcoefficients in the two equations helps describe the dependence between the twoprocesses. To ensure model flexibility and avoid unverifiable assumptions, weleave the joint distribution of the random coefficients unspecified andestimate it via nonparametric maximum likelihood. The proposal is applied todata from the Leiden 85+ study on the evolution of cognitive functioning in theelderly.

A non-homogeneous hidden Markov model for partially observed longitudinal responses