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 since dementia is assessed intermittently. So subjects can develop dementia and die between two visits without being diagnosed. To study predementia 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 sub-groups with specific risks of death, dementia, and profiles of cognitive decline. We propose Markovian and semi-Markovian versions. Both approaches are compared to a joint latent-class model for competing risks through a simulation study, and 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 subjects with dementia, mortality depends more on age than on duration of dementia. This model distinguishes the so-called terminal predeath decline (among healthy subjects) from the predementia decline.

Mixed models estimated by maximum likelihood and marginal models estimated by generalized estimating equations are the standard methods for the analysis of longitudinal data. However, their use is highly debated when attrition may be due to death. While some authors consider that mixed model estimates are interpretable only in an immortal cohort, we show that their subject-specific interpretation still holds in the population currently alive, but their population-averaged interpretation is valid only in the immortal cohort. We propose an approximation of the population-averaged mean among the population alive that highlights the difference with the population-averaged mean in the immortal cohort. The interpretation of ML estimates of mixed models and joint models for the marker and the time-to-death as well as unweighted and weighted GEE of marginal models is then illustrated in a simulation study and in an application regarding cognitive decline in the elderly.

2=0.98 in model with volume and shape). Conclusions-Our findings suggest that lesion shape contains important predictive information and reflects important environmental factors that might determine the progression of ischemia from the core. (Stroke. 2015;46:976-981.