A generalized estimator of the attributable benefit of an optimal treatment regime

For many diseases where there are several treatment options often there is no consensus on the best treatment to give individual patients. In such cases, it may be necessary to define a strategy for treatment assignment; that is, an algorithm that dictates the treatment an individual should receive based on their measured characteristics. Such a strategy or algorithm is also referred to as a treatment regime. The optimal treatment regime is the strategy that would provide the most public health benefit by minimizing as many poor outcomes as possible. Using a measure that is a generalization of attributable risk (AR) and notions of potential outcomes, we derive an estimator for the proportion of events that could have been prevented had the optimal treatment regime been implemented. Traditional AR studies look at the added risk that can be attributed to exposure of some contaminant; here we will instead study the benefit that can be attributed to using the optimal treatment strategy. We will show how regression models can be used to estimate the optimal treatment strategy and the attributable benefit of that strategy. We also derive the large sample properties of this estimator. As a motivating example, we will apply our methods to an observational study of 3856 patients treated at the Duke University Medical Center with prior coronary artery bypass graft surgery and further heart-related problems requiring a catheterization. The patients may be treated with either medical therapy alone or a combination of medical therapy and percutaneous coronary intervention without a general consensus on which is the best treatment for individual patients.