Treatment Effect Heterogeneity and Importance Measures for Multivariate Continuous Treatments

TL;DR

This paper introduces a flexible nonparametric Bayesian method to estimate and analyze heterogeneity in the effects of multivariate continuous exposures, with applications to environmental health impacts of pollutants.

Contribution

It develops novel estimands and estimation procedures for treatment effect heterogeneity in multivariate continuous exposures, filling a gap in causal inference literature.

Findings

Method accurately captures complex data generating processes.

Heterogeneity analysis reveals effect modifiers like socioeconomic status, race, and age.

Model performs well in simulated studies with diverse heterogeneity patterns.

Abstract

Estimating the joint effect of a multivariate, continuous exposure is crucial, particularly in environmental health where interest lies in simultaneously evaluating the impact of multiple environmental pollutants on health. We develop novel methodology that addresses two key issues for estimation of treatment effects of multivariate, continuous exposures. We use nonparametric Bayesian methodology that is flexible to ensure our approach can capture a wide range of data generating processes. Additionally, we allow the effect of the exposures to be heterogeneous with respect to covariates. Treatment effect heterogeneity has not been well explored in the causal inference literature for multivariate, continuous exposures, and therefore we introduce novel estimands that summarize the nature and extent of the heterogeneity, and propose estimation procedures for new estimands related to treatment effect heterogeneity. We provide theoretical support for the proposed models in the form of posterior contraction rates and show that it works well in simulated examples both with and without heterogeneity. Our approach is motivated by a study of the health effects of simultaneous exposure to the components of PM$_{2.5}$, where we find that the negative health effects of exposure to environmental pollutants are exacerbated by low socioeconomic status, race and age.