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In this paper, we undertake a case study in which interest lies in estimatinga causal exposure-response function (ERF) for long-term exposure to fineparticulate matter (PM$_{2.5}$) and respiratory hospitalizations insocioeconomically disadvantaged children using nationwide Medicaid claims data.New methods are needed to address the specific challenges the Medicaid datapresent. First, Medicaid eligibility criteria, which are largely based onfamily income for children, differ by state, creating socioeconomicallydistinct populations and leading to clustered data, where zip codes (our unitsof analysis) are nested within states. Second, Medicaid enrollees'individual-level socioeconomic status, which is known to be a confounder and aneffect modifier of the exposure-response relationships under study, is notavailable. However, two useful surrogates are available: median householdincome of each enrollee's zip code of residence and state-level Medicaid familyincome eligibility thresholds for children. In this paper, we introduce acustomized approach, called \textit{MedMatch}, that builds on generalizedpropensity score matching methods for estimating causal ERFs, adapting theseapproaches to leverage our two surrogate variables to account for potentialconfounding and/or effect modification by socioeconomic status. We conductextensive simulation studies, consistently demonstrating the strong performanceof \textit{MedMatch} relative to conventional approaches to handling thesurrogate variables. We apply \textit{MedMatch} to estimate the causal ERFbetween long-term PM$_{2.5}$ exposure and first respiratory hospitalizationamong children in Medicaid from 2000 to 2012. We find a positive association,with a steeper curve at PM$_{2.5} \le 8$ $\mu$g/m$^3$ that levels off at higherconcentrations.

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