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Biomedical studies have a common interest in assessing relationships betweenmultiple related health outcomes and high-dimensional predictors. For example,in reproductive epidemiology, one may collect pregnancy outcomes such as lengthof gestation and birth weight and predictors such as single nucleotidepolymorphisms in multiple candidate genes and environmental exposures. In suchsettings, there is a need for simple yet flexible methods for selecting truepredictors of adverse health responses from a high-dimensional set of candidatepredictors. To address this problem, one may either consider linear regressionmodels for the continuous outcomes or convert these outcomes into binaryindicators of adverse responses using pre-defined cutoffs. The former strategyhas the disadvantage of often leading to a poorly fitting model that does notpredict risk well, while the latter approach can be very sensitive to thecutoff choice. As a simple yet flexible alternative, we propose a method foradverse subpopulation regression (ASPR), which relies on a two component latentclass model, with the dominant component corresponding to (presumed) healthyindividuals and the risk of falling in the minority component characterized viaa logistic regression. The logistic regression model is designed to accommodatehigh-dimensional predictors, as occur in studies with a large number of gene byenvironment interactions, through use of a flexible nonparametric multipleshrinkage approach. The Gibbs sampler is developed for posterior computation.The methods are evaluated using simulation studies and applied to a geneticepidemiology study of pregnancy outcomes.

Adverse Subpopulation Regression for Multivariate Outcomes with High-Dimensional Predictors