Given the aging population in the UK, statistical modelling of cognitive function in the older population is of interest. Joint models are formulated for survival and cognitive function in the older population. Because tests of cognitive function often result in discrete outcomes, binomial and beta–binomial mixed effects regression models are applied to analyse longitudinal measurements. Dropout due to death is accounted for by parametric survival models, where the choice of a Gompertz baseline hazard and the specification of the random-effects structure are of specific interest. The measurement model and the survival model are combined in a shared parameter joint model. Estimation is by marginal likelihood. The methods are used to analyse data from the Cambridge City over-75s cohort study and the English Longitudinal Study of Agein
