Mixture models for the analysis of multi-state processes under coarsened observation schemes

Multi-state models offer an appealing framework for characterizing disease processes in settings where they can be meaningfully characterized into a finite number of distinct stages.  While transitions between stages occur in continuous time, such disease processes are typically under intermittent observation and so the status of individuals is only know at periodic assessment times.  We consider two settings in which multi-state processes featuring different forms of heterogeneity are under incomplete observation. Motivating studies from the University of Toronto Psoriatic Arthritis Clinic will be considered in illustrative applications.