Matching on Generalized Propensity Scores with Continuous Exposures

In the context of a binary treatment, matching is a well-established approach in causal inference. However, in the context of a continuous treatment or exposure, matching is still underdeveloped. We propose an innovative matching approach to estimate an average causal exposure-response function under the setting of continuous exposures that relies on the generalized propensity score (GPS). Our approach maintains the following attractive features of matching: a) clear separation between the design and the analysis; b) robustness to model misspecification or to the presence of extreme values of the estimated GPS; c) straightforward assessment of covariate balance. We first introduce an assumption of identifiability, called local weak unconfoundedness. Under this assumption and mild smoothness conditions, we provide theoretical guarantees that our proposed matching estimator attains point-wise consistency and asymptotic normality. In simulations, our proposed matching approach outperforms existing methods under settings of model misspecification or the presence of extreme values of the estimated GPS. We apply our proposed method to estimate the average causal exposure-response function between long-term PM$_{2.5}$ exposure and all-cause mortality among 68.5 million Medicare enrollees, 2000-2016. We found strong evidence of a harmful effect of long-term PM$_{2.5}$ exposure on mortality. Code for the proposed matching approach is provided in the CausalGPS R package, which is available on CRAN and provides a computationally efficient implementation.