Analysis of interval-censored disease progression data via multi-state models under a nonignorable inspection process.

Irreversible multi-state models provide a convenient framework for characterizing disease processes that arise when the states represent the degree of organ or tissue damage incurred by a progressive disease. In many settings, however, individuals are only observed at periodic clinic visits and so the precise times of the transitions are not observed. If the life history and observation processes are not independent, the observation process contains information about the life history process, and more importantly, likelihoods based on the disease process alone are invalid. With interval-censored failure time data, joint models are nonidentifiable and data analysts must rely on sensitivity analyses to assess the effect of the dependent observation times. This paper is concerned, however, with the analysis of data from progressive multi-state disease processes in which individuals are scheduled to be seen at periodic pre-scheduled assessment times. We cast the problem in the framework used for incomplete longitudinal data problems. Maximum likelihood estimation via an EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. Data from a cohort of patients with psoriatic arthritis are analyzed for illustration.