# Confounder-Dependent Bayesian Mixture Model: Characterizing Heterogeneity of Causal Effects in Air Pollution Epidemiology

## TL;DR

This paper introduces a Bayesian mixture model that characterizes heterogeneity in causal effects of air pollution on mortality, identifying distinct vulnerable groups based on population characteristics.

## Contribution

It proposes a novel confounder-dependent Bayesian mixture model leveraging the dependent Dirichlet process to identify and analyze heterogeneous causal effect groups.

## Key findings

- Identified six mutually exclusive groups with different causal effects of PM2.5 on mortality.
- Demonstrated the model's effectiveness through simulations.
- Applied the method to Medicare data revealing heterogeneity in vulnerability.

## Abstract

Several epidemiological studies have provided evidence that long-term exposure to fine particulate matter (PM2.5) increases mortality risk. Furthermore, some population characteristics (e.g., age, race, and socioeconomic status) might play a crucial role in understanding vulnerability to air pollution. To inform policy, it is necessary to identify groups of the population that are more or less vulnerable to air pollution. In causal inference literature, the Group Average Treatment Effect (GATE) is a distinctive facet of the conditional average treatment effect. This widely employed metric serves to characterize the heterogeneity of a treatment effect based on some population characteristics. In this work, we introduce a novel Confounder-Dependent Bayesian Mixture Model (CDBMM) to characterize causal effect heterogeneity. More specifically, our method leverages the flexibility of the dependent Dirichlet process to model the distribution of the potential outcomes conditionally to the covariates and the treatment levels, thus enabling us to: (i) identify heterogeneous and mutually exclusive population groups defined by similar GATEs in a data-driven way, and (ii) estimate and characterize the causal effects within each of the identified groups. Through simulations, we demonstrate the effectiveness of our method in uncovering key insights about treatment effects heterogeneity. We apply our method to claims data from Medicare enrollees in Texas. We found six mutually exclusive groups where the causal effects of PM2.5 on mortality are heterogeneous.