Why prefer double robust estimators in causal inference?

Abstract

In point treatment studies, causal parameters defined by marginal structural models can be estimated under the assumption of no unobserved confounders. Three estimators can be used: the G-computation, inverse probability of treatment weighted (IPTW) or double robust (DR) estimator. The consistency properties of the IPTW and DR estimators are known under an assumption on the treatment mechanism that we name the“Experimental Treatment Assignment” (ETA) assumption. We first propose to extend the consistency property of the DR estimator by redefining the DR estimating function when the ETA assumption is violated. With simulations emulating point treatment studies, we then illustrate the practical consequences of the redefinition of the DR estimator: IPTW estimates are biased at finite sample size when the ETA assumption is practically or theoretically violated, whereas the finite sample bias for the DR estimates is negligible under correct model specifications. While DR estimators are known to be more robust than IPTW estimators, this result implies that they are also more robust than G-computation estimators in point treatment studies. These results motivated the development of a methodology to construct such redefined DR estimators for a general missing data structure. We conclude with an illustration of the rationale of this general methodology with causal inference in point treatment studies.