Title: Convex mixture regression for quantitative risk assessment
Authors: Daniele Durante - University of Padova (Italy) [presenting]
Antonio Canale - University of Padua (Italy)
David Dunson - Duke University (United States)
Abstract: There is a considerable interest in studying how the distribution of an outcome varies with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A fundamental focus is inference on the dose levels associated with a particular increase in risk relative to a baseline. Current methodologies either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. These choices may lead to a loss of information and provide a restrictive characterization of the dose--response relation. We instead propose a class of convex mixture regression models that allow the entire distribution of the outcome to be unknown and changing with the dose. To avoid overfitting, we rely on a flexible characterization of the density at the extreme dose levels, and express the conditional density at each intermediate dose as a convex combination of the extremal densities. This representation generalizes popular dose--response models for binary outcomes and facilitates inference on extra risk functions of interest in quantitative risk assessments with continuous outcomes. We develop simple Markov chain Monte Carlo algorithms for implementation, and propose goodness-of-fit assessments. The benefits of our methods are highlighted in simulations and in a study on the impact of dioxin exposure on preterm birth.