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Constructing a confidence interval for the fraction who benefit from treatment, using randomized trial data
Author(s) -
Huang Emily J.,
Fang Ethan X.,
Hanley Daniel F.,
Rosenblum Michael
Publication year - 2019
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13101
Subject(s) - confidence interval , fraction (chemistry) , randomized controlled trial , statistics , mathematics , interval (graph theory) , medicine , computer science , combinatorics , chromatography , chemistry
The fraction who benefit from treatment is the proportion of patients whose potential outcome under treatment is better than that under control. Inference on this parameter is challenging since it is only partially identifiable, even in our context of a randomized trial. We propose a new method for constructing a confidence interval for the fraction, when the outcome is ordinal or binary. Our confidence interval procedure is pointwise consistent. It does not require any assumptions about the joint distribution of the potential outcomes, although it has the flexibility to incorporate various user‐defined assumptions. 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, which can be computed efficiently using optimization tools. In simulation, our method attains the nominal coverage probability or higher, and can have narrower average width than competitor methods. We apply it to a trial of a new intervention for stroke.