Joint latent class model for longitudinal data and interval-censored semi-competing events: Application to dementia

Joint models are used in ageing studies to investigate the association between longitudinal markers and a time-to-event, and have been extended to multiple markers and/or competing risks. The competing risk of death must be considered in the elderly because death and dementia have common risk factors. Moreover, in cohort studies, time-to-dementia is interval-censored because dementia is only assessed intermittently. So subjects can become demented and die between two follow-up visits without being diagnosed. To study pre-dementia cognitive decline, we propose a joint latent class model combining a (possibly multivariate) mixed model and an illness-death model handling both interval censoring (by accounting for a possible unobserved transition to dementia) and semi-competing risks. Parameters are estimated by maximum likelihood handling interval censoring. The correlation between the marker and the times-to-events is captured by latent classes, homogeneous groups with specific risks of death and dementia and profiles of cognitive decline. We propose markovian and semi-markovian versions. Both approaches are compared to a joint latent class model for standard competing risks through a simulation study, and then applied in a prospective cohort study of cerebral and functional ageing to distinguish different profiles of cognitive decline associated with risks of dementia and death. The comparison highlights that among demented subjects, mortality depends more on age than duration of dementia. This model distinguishes the so-called terminal pre-death decline (among non-demented subjects) from the pre-dementia decline.