Abstract

Chemical exposure has become an important concern for public health in recent decades with certain exposures being linked to health issues such as cardiovascular heart disease (CVD). However, individuals are usually exposed to multiple chemicals depending on environmental, economic, and air quality factors. Thus a model that both measures the associations among chemicals and their relations with health outcomes is warranted. For example, biomonitoring measures that track individual chemical exposure levels through blood and urine samples can be used to learn which exposures are predictive of certain health indicators. The associations between the chemical exposure levels can be represented by an undirected graph and the structure of that graph exploited to understand the associations between the exposures and the response. In this talk, we present a sparse overlapping group lasso incorporating graphical structure (SGLIG) to regularize such a model and identify those chemical exposures most predictive of, say, CVD. Our method decomposes the coefficient estimates into a sum of latent variables, corresponding to the sum of each exposure’s contribution to the coefficient vector, and performs regularization on the latent variables rather than on the coefficient vector directly. We use a novel proximal projection to facilitate optimization of the objective function and demonstrate its stable performance and scalability in simulation and on real world data.