Nonparametric Methods for Doubly Robust Estimation of Continuous Treatment Effects

• Activity Number: 33
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Edward Kennedy* and Zongming Ma and Matthew McHugh and Dylan Small
• Companies: University of Pennsylvania Perelman School of Medicine and The Wharton School and University of Pennsylvania and University of Pennsylvania
• Keywords: causal inference ; cross-validation ; dose-response ; efficient influence function ; semiparametric

Abstract

In this work we consider the problem of estimating the marginal causal effect of a continuous treatment without imposing parametric assumptions on the form of that effect. Continuous treatments arise often in practice (e.g., dose, duration, frequency), but available causal effect estimators require either parametric models for the effect curve or consistent estimation of a single nuisance function. We therefore propose a novel doubly robust kernel smoothing approach, which only relies on the treatment effect curve satisfying mild smoothness conditions. We show that our proposed estimators are consistent and asymptotically normal, and doubly robust since only one of two nuisance functions needs to be estimated well. As in standard nonparametric regression, the estimators converge at slower than root-n rates. We also propose a data-driven approach for choosing smoothing parameter values, and illustrate our methods via simulation and in a study of the effect of nurse staffing on hospital readmissions penalties.