In many randomized controlled trials, the primary analysis focuses on the average treatment effect and does not address whether treatment benefits are widespread or limited to a select few. This problem affects many disease areas, since it stems from how randomized trials, often the gold standard for evaluating treatments, are designed and analyzed. Our goal is to learn about the fraction who benefit from a new treatment using randomized trial data. We consider the case where the outcome is ordinal, with binary outcomes as a special case. In general, the fraction who benefit is non-identifiable, and the best that can be obtained are sharp lower and upper bounds. Our contributions include (i) proving the plug-in estimator of the bounds can be inconsistent if support restrictions are made on the joint distribution of the potential outcomes; (ii) developing the first consistent estimator for this case; and (iii) applying this estimator to a randomized trial of a medical treatment to determine whether the estimates can be informative. Our estimator is computed using linear programming, allowing fast implementation. R code is provided.

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