Causal Inference for Semiparametric Regression Models Using Higher-order Influence Functions

• Activity Number: 516
• Type: Contributed
• Date/Time: Thursday, August 11, 2005 : 10:30 AM to 12:20 PM
• Sponsor: General Methodology
• Author(s): Lingling Li*+
• Companies: Harvard University
• Keywords: causal inference ; semiparametric regression ; higher order influence functions ; doubly robust

Abstract

Consider the semiparametric regression model E[Y|R,X]=b*R+w(X). R is a dichotomous treatment variable, X is a high-dimensional (say 60) vector of confounders, and w(X) is an unknown function of X. Recent developments in semiparametric theory have lead to doubly robust (DR) estimators for the parameter b. Double robustness guarantees n1/2 consistency (the standard parametric rate) of our estimator for b as a long as (a) there is no unmeasured confounding and (b) either (but not necessarily both) a working model for the propensity score or a working regression model of Y on R and X are correctly specified. DR estimation will fail to be consistent if both (a) and (b) are not sufficiently close to guarantee small bias. We present novel confidence intervals for the treatment effect based on higher-order influence functions. Given any smoothness assumption placed on (a) and (b), our new theory yields valid confidence intervals for the true treatment effect beyond the scope of what DR can achieve; however, we sacrifice n1/2 consistency for slower convergence rates as commonly encountered in nonparametric inference. We present simulation results demonstrating the performance of our method.