Statistical Methods for the Fraction who Benefit using a Randomized Trial

I develop new statistical methods to learn the fraction who benefit from treatment, using randomized trial data. Defined in the potential outcomes framework, the fraction who benefit is the proportion of patients whose potential outcome under treatment is better than that under control. Since only one potential outcome can be observed for any given person, this fraction is a non-identifiable parameter unless strong assumptions are made about the joint probability distribution of the potential outcomes. A strength of my methods is that they do not require assumptions about the joint distribution, but can incorporate a wide range of user-defined assumptions based on subject matter knowledge. I derive sharp lower and upper bounds on the fraction and develop a method to estimate these bounds, which is consistent and computationally efficient. The method is illustrated through an application to the MISTIE II (Minimally Invasive Surgery for Intracerebral Hemorrhage Evacuation Phase II) randomized trial on intracerebral hemorrhage. In addition, I develop a method to construct a confidence interval for the fraction who benefit, and prove that it is pointwise consistent. The method is demonstrated through an application to the CLEAR III (Clot Lysis: Evaluating Accelerated Resolution of Intraventricular Haemorrhage III) randomized trial on intraventricular hemorrhage