Environmental health studies are increasingly measuring multiple pollutants to characterize the joint health effects attributable to exposure mixtures. However, the underlying dose-response relation- ship between toxicants and health outcomes of interest may be highly nonlinear, with possible nonlinear interaction effects. We present hierarchical integrative group LASSO (HiGLASSO), a general shrinkage and selection framework to identify noteworthy nonlinear main and interaction. HiGLASSO is broadly applicable for studying potential nonlinear main and interaction effects in the presence of group structures among a set of exposures.
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