Doubly robust estimators are an approach used for estimating causal effects, usually based on fitting 2 statistical models (1). As the initial motivating example, Scharfstein et al. defined a robust estimator of the causal effect of some exposure X on outcome Y using models for both X and Y; they demonstrated that such an estimator is consistent if “at least one of the [fitted] models… is correct” (2, p. 1142). Such estimators were later termed “doubly robust” (3, p. 6). Here, we demonstrate that using common (but incorrect) intuition about what makes a model “correct” or “incorrect” can turn doubly robust estimators into estimators that are inconsistent if at least one of the fitted models is wrong. We introduce and resolve this double-robust paradox, demonstrating what must be meant by “correct model.
