Infinite-Dimensional Causal Models

• Activity Number: 325
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Edward Kennedy*+
• Keywords: causal inference ; nonparametric regression ; semiparametric theory

Abstract

We consider the problem of estimating causal quantities that cannot be characterized by finite-dimensional real-valued parameters. The classical approach in causal inference has been to either restrict interest to quantities that are necessarily low-dimensional (e.g., marginal effects of binary treatments), or else to assume a parametric model when the quantity of interest is a possibly complicated function. Our contribution in this work is to develop a doubly robust approach for estimation of infinite-dimensional causal quantities, keeping the quantity itself as the parameter of interest, and without resorting to modeling assumptions. We do so using a smoothing technique, which yields estimators that converge at slower than parametric root-n rates. We discuss the approach with several examples, estimating the effects of: a continuous treatment (such as a dose or duration), a binary treatment in the presence of a continuous effect modifier, and a complex time-varying treatment. We also provide an illustration in a real data application investigating the effect of erythropoietin among patients with chronic kidney disease.