Multivariate incremental effects for continuous treatments: Studying the health effects of environmental mixtures

TL;DR

This paper introduces a new causal inference framework for evaluating health effects of multivariate continuous exposures like air pollution mixtures, overcoming positivity violations and enabling policy-relevant estimands.

Contribution

It extends exponential tilting to multivariate exposures, develops efficient estimation algorithms, and applies the framework to real environmental health data.

Findings

Identified optimal strategies for reducing adverse health outcomes from PM2.5 mixtures.

Developed a Riemannian BFGS algorithm for constrained optimization.

Established asymptotic normality and efficiency bounds for estimators.

Abstract

Evaluating the causal health effects of multivariate, continuous exposures, such as air pollution mixtures, is a critical public health challenge. A primary obstacle is the frequent violation of the positivity assumption, which renders the effects of standard deterministic interventions unidentified or heavily reliant on unreliable model extrapolation. In this paper, we develop a novel causal inference framework to address this challenge. We extend exponential tilting to multivariate exposures and address the critical question of how to compare different intervention directions fairly. This establishes a systematic framework for defining and evaluating various policy-relevant causal estimands, allowing researchers to address diverse scientific questions. We develop numerous methodological advancements, including efficient one-step estimation strategies, a Riemannian BFGS algorithm to solve a constrained manifold optimization problem, semiparametric efficiency bounds for causal estimands, minimax rates for estimators, and establishing asymptotic normality. We demonstrate our framework's utility by applying it to a nationwide environmental health dataset to identify the optimal strategy for reducing adverse health outcomes associated with a PM$_{2.5}$ chemical mixture.