A doubly robust estimator for the attributable benefit of a treatment regime

The identification and study of treatment regimes (algorithms or policies for dictating treatments to patients) are a growing area of study in the statistical sciences. Many methods have been put forth to identify the 'best' or optimal treatment regime from observed data. Once the optimal treatment regime is identified, a secondary question of interest is to determine the public health impact of that health policy. Simply put, what is the benefit that can be attributed to using such a regime in practice? The attributable benefit of a treatment regime is a measure of the reduction in poor outcomes that would have been observed had the regime of interest been utilized. Methods for identifying the optimal treatment regime can use statistical modeling techniques which are susceptible to model misspecification in the identification of both the optimal treatment regime and its attributable benefit. Using notions from causal inference and building upon previous work, this paper identifies an estimator for attributable benefit that offers a second layer of protection in cases where an outcome regression model may be misspecified. The estimator is dubbed doubly robust in that it is unbiased for the true benefit if either a model for the outcome or a propensity model for treatment is correctly specified. Large sample properties are explored, and two sets of confidence intervals proposed. Simulation studies compare the proposed estimator with previous work, with a focus on model misspecification. The estimator is applied to real data to examine its utility in practice.