  Traditional regulations of chemical exposure tend to focus on single
exposures, overlooking the potential amplified toxicity due to multiple
concurrent exposures. We are interested in understanding the average outcome if
exposures were limited to fall under a multivariate threshold. Because
threshold levels are often unknown a priori, we provide an algorithm that finds
exposure threshold levels where the expected outcome is maximized or minimized.
Because both identifying thresholds and estimating policy effects on the same
data would lead to overfitting bias, we also provide a data-adaptive estimation
framework, which allows for both threshold discovery and policy estimation.
Simulation studies show asymptotic convergence to the optimal exposure region
and to the true effect of an intervention. We demonstrate how our method
identifies true interactions in a public synthetic mixture data set. Finally,
we applied our method to NHANES data to discover metal exposures that have the
most harmful effects on telomere length. We provide an implementation in the
CVtreeMLE R package.
