The fraction who benefit from treatment is defined as the proportion of patients whose potential outcome under treatment is better than that under control. Statistical inference for this parameter is challenging since it is only partially identifiable, even in our context of a randomized trial. We propose and evaluate a new method for constructing a confidence interval for the fraction who benefit, when the outcome is ordinal-valued (with binary outcomes as a special case). This confidence interval procedure is proved to be pointwise consistent. Our method does not require any assumptions about the joint distribution of the potential outcomes, although it has the flexibility to incorporate a wide range of user-defined assumptions. A potential advantage of our approach is that, unlike existing confidence interval methods for partially identified parameters (such as m-out-of-n bootstrap and subsampling), we do not need to select m or the subsample size, which is generally a challenging problem. Our method is based on a stochastic optimization technique involving a second order, asymptotic approximation that, to the best of our knowledge, has not been applied to biomedical studies. This approximation leads to statistics that are solutions to quadratic programs, and so they can be computed efficiently using existing optimization tools. In all of our simulations, our method attains the nominal coverage probability or higher, and can have substantially narrower average width compared to the m-out-of-n bootstrap. We also apply our method to a completed trial data set of a new surgical intervention for severe stroke.


Biostatistics | Statistical Methodology

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