Bayesian semiparametric joint modeling of longitudinal explanatory variables of mixed types and a binary outcome.

Many prospective biomedical studies collect longitudinal clinical and lifestyle data that are both continuous and discrete. In some studies, there is interest in the association between a binary outcome and the values of these longitudinal measurements at a specific time point. A common problem in these studies is inconsistency in timing of measurements and missing follow-ups which can lead to few measurements at the time of interest. Some methods have been developed to address this problem, but are only applicable to continuous measurements. To address this limitation, we propose a new class of joint models for a binary outcome and longitudinal explanatory variables of mixed types. The longitudinal model uses a latent normal random variable construction with regression splines to model time-dependent trends in mean with a Dirichlet Process prior assigned to random effects to relax distribution assumptions. We also standardize timing of the explanatory variables by relating the binary outcome to imputed longitudinal values at a set time point. The proposed model is evaluated through simulation studies and applied to data from a cancer survivor study of participants in the Women's Health Initiative.