A joint model for longitudinal outcomes and longitudinal covariates

In biomedical research, often hierarchical binary and continuous responses need to be jointly modeled. In joint generalized linear mixed models this can be done by allowing the random effects of both models to correlate. In this model the association structure between the various responses and the evolution of this association over time can be examined. Still, investigating this association is often limited to scrutinizing the latent correlations between the random effects. In addition, the interpretation of this hierarchical model is subject-specific since it is conditional on random effects. In my PhD this approach is extended and it is shown how manifest correlations can be computed, which are the associations between the observed responses. Further, a marginal model is formulated, in which the interpretation is no longer conditional on the random effects. In addition, prediction intervals are derived of one subvector of responses conditional on the other. These methods are applied in several case studies, with for example an application in a study of the lung function and allergic bronchopulmonary aspergillosis in patients with cystic fibrosis.