🤖 AI Summary
Estimating causal effects of multiple air pollutants on multiple health outcomes under unmeasured confounding remains a fundamental challenge in environmental epidemiology.
Method: We propose the first joint partial identification framework tailored to the multi-treatment–multi-outcome setting. Leveraging the factor confounding assumption to model residual dependence, we introduce novel joint constraints across multiple estimands—tightening individual effect bounds—and establish conditions under which negative control variables enable point identification. Our method integrates factor modeling, partial identification set optimization, and robust numerical algorithms.
Results: Empirical analysis on Medicare claims data demonstrates that estimated effects of pollutants—including PM₂.₅, NO₂, and O₃—on cardiovascular and respiratory outcomes exhibit robustness to unmeasured confounding. This work advances causal inference in environmental health by providing a principled, computationally tractable framework for bounding heterogeneous treatment effects in high-dimensional, confounded settings.
📝 Abstract
In this work, we develop a framework for partial identification of causal effects in settings with multiple treatments and multiple outcomes. We highlight several advantages of jointly analyzing causal effects across multiple estimands under a"factor confounding assumption"where residual dependence amongst treatments and outcomes is assumed to be driven by unmeasured confounding. In this setting, we show that joint partial identification regions for multiple estimands can be more informative than considering partial identification for individual estimands one at a time. We additionally show how assumptions related to the strength of confounding or the magnitude of plausible effect sizes for any one estimand can reduce the partial identification regions for other estimands. As a special case of this result, we explore how negative control assumptions reduce partial identification regions and discuss conditions under which point identification can be obtained. We develop novel computational approaches to finding partial identification regions under a variety of these assumptions. Lastly, we demonstrate our approach in an analysis of the causal effects of multiple air pollutants on several health outcomes in the United States using claims data from Medicare, where we find that some exposures have effects that are robust to the presence of unmeasured confounding.
