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Exposure to mixtures of chemicals, such as drugs, pollutants, and nutrients,is common in real-world exposure or treatment scenarios. To understand theimpact of these exposures on health outcomes, an interpretable and importantapproach is to estimate the causal effect of exposure regions that are mostassociated with a health outcome. This requires a statistical estimator thatcan identify these exposure regions and provide an unbiased estimate of acausal target parameter given the region. In this work, we present amethodology that uses decision trees to data-adaptively determine exposureregions and employs cross-validated targeted maximum likelihood estimation tounbiasedly estimate the average regional-exposure effect (ARE). This results ina plug-in estimator with an asymptotically normal distribution and minimumvariance, from which confidence intervals can be derived. The methodology isimplemented in the open-source software, CVtreeMLE, a package in R. Analystsput in a vector of exposures, covariates and an outcome and tables are givenfor regions in the exposures, such as lead > 2.1 & arsenic > 1.4, with anassociated ARE which represents the mean outcome difference if all individualswere exposed to this region compared to if none were exposed to this region.CVtreeMLE enables researchers to discover interpretable exposure regions inmixed exposure scenarios and provides robust statistical inference for theimpact of these regions. The resulting quantities offer interpretablethresholds that can inform public health policies, such as pollutantregulations, or aid in medical decision-making, such as identifying the mosteffective drug combinations.

Cross-Validated Decision Trees with Targeted Maximum Likelihood Estimation for Nonparametric Causal Mixtures Analysis