Efficient Estimation of Modified Treatment Policy Effects Based on the Generalized Propensity Score

Abstract

Continuous treatment variables have posed a significant challenge for causal inference, both in the formulation and identification of causal effects and in their robust estimation. Traditionally, focus has been placed on techniques applicable to binary or categorical treatments with few levels, settings allowing the application of propensity score-based methodology with relative ease. Efforts to accommodate continuous treatments introduced the generalized propensity score (the conditional density of treatment given covariates), a nuisance parameter required for estimation of scientifically informative parameters like the causal dose-response curve and the causal effects of modified treatment policies (stochastic interventions that shift the value of the treatment actually received). As conditional density functionals are challenging to estimate, the vast majority of generalized propensity score estimators impose restrictive modeling assumptions, sharply limiting the real-world applicability of both inverse probability weighted (IPW) and doubly robust estimators alike. To overcome this, we present a flexible estimator of the generalized propensity score based on the highly adaptive lasso, a nonparametric regression function with rate-convergence properties suitable for the construction of asymptotically linear and efficient estimators . Using our proposed estimator, we detail the construction of nonparametric IPW estimators of the causal effects of modified treatment policies as well as both targeted and global undersmoothing criteria for the selection of asymptotically efficient IPW estimators. Through numerical experiments, we demonstrate several variants of our IPW estimators exhibit desirable performance. We briefly introduce the haldensify R package, which implements our proposals for generalized propensity score and nonparametric IPW estimation.