  There is abundant interest in assessing the joint effects of multiple
exposures on human health. This is often referred to as the mixtures problem in
environmental epidemiology and toxicology. Classically, studies have examined
the adverse health effects of different chemicals one at a time, but there is
concern that certain chemicals may act together to amplify each other's
effects. Such amplification is referred to as synergistic interaction, while
chemicals that inhibit each other's effects have antagonistic interactions.
Current approaches for assessing the health effects of chemical mixtures do not
explicitly consider synergy or antagonism in the modeling, instead focusing on
either parametric or unconstrained nonparametric dose response surface
modeling. The parametric case can be too inflexible, while nonparametric
methods face a curse of dimensionality that leads to overly wiggly and
uninterpretable surface estimates. We propose a Bayesian approach that
decomposes the response surface into additive main effects and pairwise
interaction effects, and then detects synergistic and antagonistic
interactions. Variable selection decisions for each interaction component are
also provided. This Synergistic Antagonistic Interaction Detection (SAID)
framework is evaluated relative to existing approaches using simulation
experiments and an application to data from NHANES.
