Adverse subpopulation regression for multivariate outcomes with high-dimensional predictors

Biomedical studies have a common interest in assessing relationships between multiple related health outcomes and high-dimensional predictors. For example, in reproductive epidemiology, one may collect pregnancy outcomes such as length of gestation and birth weight and predictors such as single nucleotide polymorphisms in multiple candidate genes and environmental exposures. In such settings, there is a need for simple yet flexible methods for selecting true predictors of adverse health responses from a high-dimensional set of candidate predictors. To address this problem, one may either consider linear regression models for the continuous outcomes or convert these outcomes into binary indicators of adverse responses using predefined cutoffs. The former strategy has the disadvantage of often leading to a poorly fitting model that does not predict risk well, whereas the latter approach can be very sensitive to the cutoff choice. As a simple yet flexible alternative, we propose a method for adverse subpopulation regression, which relies on a two-component latent class model, with the dominant component corresponding to (presumed) healthy individuals and the risk of falling in the minority component characterized via a logistic regression. The logistic regression model is designed to accommodate high-dimensional predictors, as occur in studies with a large number of gene by environment interactions, through the use of a flexible nonparametric multiple shrinkage approach. The Gibbs sampler is developed for posterior computation. We evaluate the methods with the use of simulation studies and apply these to a genetic epidemiology study of pregnancy outcomes.