A joint model for interval-censored functional decline trajectories under informative observation

Multi-state models are useful for modelling disease progression where the state space of the process is used to represent the discrete disease status of subjects. Often, the disease process is only observed at clinical visits, and the schedule of these visits can depend on the disease status of patients. In such situations, the frequency and timing of observations may depend on transition times that are themselves unobserved in an interval-censored setting. There is a potential for bias if we model a disease process with informative observation times as a non-informative observation scheme with pre-specified examination times. In this paper, we develop a joint model for the disease and observation processes to ensure valid inference because the follow-up process may itself contain information about the disease process. The transitions for each subject are modelled using a Markov process, where bivariate subject-specific random effects are used to link the disease and observation models. Inference is based on a Bayesian framework, and we apply our joint model to the analysis of a large study examining functional decline trajectories of palliative care patients.