A joint model for a longitudinal outcome and a progressive multistate model under a mixed observation scheme

Joint models for longitudinal and event-time data can be used to understand the co-development of multiple correlated non-fatal outcomes, such as those encountered when studying diabetic microvascular complications. However, such models were not developed for event-times characterized by a multistate process where the entry time into certain states is interval-censored, which is an important feature of interval cohort study designs. Our aim was to develop a joint model for this setting. Specifically, we formulated a shared random effects joint model with linear mixed-effects and proportional intensities progressive three-state Markov submodels, with interval-censoring of entry into the transient state and exact observation of entry into the absorbing state. Maximum likelihood estimation was used, with exploration of the functional forms and association structures. Bias and confidence interval coverage of the model parameters were assessed using simulation, and performance was compared to existing approaches that assume exact observation of all entry times, which were found to sometimes overestimate the magnitude of association between the longitudinal and multistate outcomes. In an application of the model, the trajectory of a routinely measured diabetic complication (retinopathy) was associated with progression through states of a more difficult to measure complication (neuropathy), suggesting potential efficiencies in screening and monitoring.