Joint Bayesian longitudinal models for mixed outcome types and associated model selection techniques

Motivated by data measuring progression of leishmaniosis in a cohort of US dogs, we develop a Bayesian longitudinal model with autoregressive errors to jointly analyze ordinal and continuous outcomes. Multivariate methods can borrow strength across responses and may produce improved longitudinal forecasts of disease progression over univariate methods. We explore the performance of our proposed model under simulation, and demonstrate that it has improved prediction accuracy over traditional Bayesian hierarchical models. We further identify an appropriate model selection criterion. We show that our method holds promise for use in the clinical setting, particularly when ordinal outcomes are measured alongside other variables types that may aid clinical decision making. This approach is particularly applicable when multiple, imperfect measures of disease progression are available.