A Bayesian model for the common effects of multiple predictors on mixed outcomes.

We propose a Bayesian multivariate model in which a single linear combination of the covariates predict multiple outcomes simultaneously. The single linear combination is a data-derived score along the lines of the Apache or Charlson index scores for critically ill patients, the Karnofsky or Eastern Cooperative Oncology Group score for cancer patients or Euro-score for cardiac patients that may be used to predict multiple outcomes. Outcomes may be discrete or continuous and we use a composition of generalized linear models for the marginal distribution for each outcome. We explain how to set the prior distribution and we use Markov chain Monte Carlo methods to calculate the posterior distribution. We propose two types of expanded models to diagnose whether each outcome indeed has predictor effects common with the other outcomes, and whether a particular predictor is commonly predictive for all outcomes. We determine a final model based on the diagnostic models. The method is applied to a study yielding multiple psychometric outcomes of mixed type measured in young people living with human immunodeficiency virus.