Improved Doubly Robust Estimation in Marginal Mean Models for Dynamic Regimes

Abstract

Doubly robust (DR) estimators are an important class of statistics derived from a theory of semiparametric efficiency. They have become a popular tool in causal inference, including applications to dynamic treatment regimes. The doubly robust estimators for the mean response to a dynamic treatment regime may be conceived through the augmented inverse probability weighted (AIPW) estimating function, defined as the sum of the inverse probability weighted (IPW) estimating function and an augmentation term. The IPW estimating function of the causal estimand via marginal structural model is defined as the complete-case score function for those subjects whose treatment sequence is consistent with the dynamic regime in question divided by the probability of observing the treatment sequence given the subject's treatment and covariate histories. The augmentation term is derived by projecting the IPW estimating function onto the nuisance tangent space and has mean-zero under the truth. The IPW estimator of the causal estimand is consistent if (i) the treatment assignment mechanism is correctly modeled and the AIPW estimator is consistent if either (i) is true or (ii) nested functions of intermediate and final outcomes are correctly modeled.

Keywords

• causal inference
• informative eligibility
• missing data
• treatment competing events
• 92b15