Joint models for bivariate discrete longitudinal outcome and survival

In analytical studies of longitudinal and time-to-event data, measuring the relationship between longitudinal outcomes and the time of event occurring simultaneously is of interest. It is common in medical statistics to have non-negative integers as longitudinal responses, and there will often be more than one response variable in the data. The main aim of this thesis is to construct the corresponding bivariate joint models to analyse these discrete longitudinal and time-to-event data. We construct two types of joint models, namely the bivariate shared random-effects joint model and the bivariate latent-class joint model. For the longitudinal model, we use extensions of the binomial distribution and the categorical distribution. In addition, to deal with attrition due to death or dementia, we use the exponential hazard model, the Weibull hazard model and the Gompertz hazard model as the survival model. We will assume that the longitudinal model and the survival model are independent of each other conditional on random effects. The joint models are applied to analyse three datasets. The first data is the English Longitudinal Study of Ageing (ELSA). The second is the PAQUID data, whose full title is PAQUID: Longitudinal data on cognitive and physical aging in the elderly. The third is PBC2: Mayo Clinic primary biliary cirrhosis data