Independence conditions and the analysis of life history studies with intermittent observation

Multistate models provide a powerful framework for the analysis of life history processes when the goal is to characterize transition intensities, transition probabilities, state occupancy probabilities, and covariate effects thereon. Data on such processes are often only available at random visit times occurring over a finite period. We formulate a joint multistate model for the life history process, the recurrent visit process, and a random loss to follow-up time at which the visit process terminates. This joint model is helpful when discussing the independence conditions necessary to justify the use of standard likelihoods involving the life history model alone and provides a basis for analyses that accommodate dependence. We consider settings with disease-driven visits and routinely scheduled visits and develop likelihoods that accommodate partial information on the types of visits. Simulation studies suggest that suitably constructed joint models can yield consistent estimates of parameters of interest even under dependent visit processes, providing the models are correctly specified; identifiability and estimability issues are also discussed. An application is given to a cohort of individuals attending a rheumatology clinic where interest lies in progression of joint damage.