Causal exposure-response curve estimation with surrogate confounders: a study of air pollution and children's health in Medicaid claims data

Abstract

In this paper, we undertake a case study to estimate a causal exposure-response function (ERF) for long-term exposure to fine particulate matter (PM$_{2.5}$) and respiratory hospitalizations in socioeconomically disadvantaged children using nationwide Medicaid claims data. These data present specific challenges. First, family income-based Medicaid eligibility criteria for children differ by state, creating socioeconomically distinct populations and leading to clustered data. Second, Medicaid enrollees' socioeconomic status, a confounder and an effect modifier of the exposure-response relationships under study, is not measured. However, two surrogates are available: median household income of each enrollee's zip code and state-level Medicaid family income eligibility thresholds for children. We introduce a customized approach for causal ERF estimation called MedMatch, building on generalized propensity score (GPS) matching methods. MedMatch adapts these methods to (1) leverage the surrogate variables to account for potential confounding and/or effect modification by socioeconomic status and (2) address practical challenges presented by differing exposure distributions across clusters. We also propose a new hyperparameter selection criterion for MedMatch and traditional GPS matching methods. Through extensive simulation studies, we demonstrate the strong performance of MedMatch relative to conventional approaches in this setting. We apply MedMatch to estimate the causal ERF between PM$_{2.5}$ and respiratory hospitalization among children in Medicaid, 2000-2012. We find a positive association, with a steeper curve at lower PM$_{2.5}$ concentrations that levels off at higher concentrations.