Doubly robust estimators are a relatively new method of estimating the average causal effect of an exposure. While this approach has been described in the statistical literature, it is not yet well known among the broader research community. Prior simulations have confirmed that the doubly robust estimator is unbiased when a confounder is omitted from 1 (but not both) of the component models (3
). Our own work confirms that this extends to less extreme scenarios in which 1 of the 2 component models has been misspecified by categorizing a continuous confounder (24
). The SAS macro described in Web Appendix 2 gives researchers a tool for implementing doubly robust estimation with bootstrapped standard errors and confidence intervals. The simulations presented here indicate that bootstrapped confidence intervals performed well across a range of sample sizes assuming at least 1 of the models was correctly specified.
There are some other attractive features of this estimator that are not directly due to the doubly robust property. Because the doubly robust estimator for the effect of exposure is calculated by averaging over the expected response for each individual under both exposure conditions, the effect estimates apply to the total population and have a marginal interpretation similar to that from a randomized trial. The particular doubly robust estimator described here incorporates flexibility by modeling the effects of covariates within levels of the exposure, which may improve control of confounding in situations where the effect of a confounder on the outcome differs by exposure group. The doubly robust estimator simultaneously produces relative and absolute effect estimates. The ease with which one can estimate absolute risks and risk differences could facilitate reporting of these effects along with the usual ratio measures and encourage researchers to more fully interpret their findings on both scales. The usual IPW estimator also shares these attractive properties with the doubly robust estimator, but the “augmentation” that makes this estimator doubly robust also makes it more efficient than the usual IPW estimator (20
As with any new method, caution is warranted. The doubly robust estimator is generally less
efficient than the maximum likelihood estimator with a correctly specified model. Thus, there is a trade-off to consider between potentially reducing bias at the expense of precision (20
). In the context of IPW estimators, it is known that weights for individuals with unusual combinations of characteristics and exposures can lead to unstable estimates with relatively large standard errors (19
). It is not yet known whether the methods for handling these influential observations (stabilized and truncated weights (19
) or trimming observations (25
)) would be effective in the context of this doubly robust estimator or if other methods of diagnosing and mitigating this bias are required. Moreover, when both models are misspecified, the resulting effect estimate may be more biased than that of a single, misspecified maximum likelihood model (26
Many aspects of applied doubly robust analysis have not yet been adequately evaluated, including strategies for selecting covariates for inclusion in the component models; diagnostics; methods for detecting and handling effect measure modification; and reconciling differences between effect estimates from doubly robust, IPW, PS, and maximum likelihood methods. In light of these unknowns, researchers should consider this analytic method a complement to rather than a substitute for other methods. We hope that rigorous examination of this method in simulations will provide the field with sound recommendations regarding best practices for its use. Given that we rarely know the true relations among exposure, outcome, and confounders, doubly robust estimators represent an important advance in methods for estimating causal effects from observational data.