title: Inequality in treatment benefits: Can we determine if a new treatment benefits the many or the few?
abstract: 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.
authors.affiliation: Department of Biostatistics, Johns Hopkins University, 615 North Wolfe Street, Baltimore, Maryland 21205, USAehuang19@jhu.edu.
authors.forename: Emily J
authors.initials: EJ
authors.lastname: Huang
authors.affiliation: Department of Statistics, Department of Industrial and Manufacturing Engineering, Pennsylvania State University, Thomas Building, University Park, Pennsylvania 16802, USA.
authors.forename: Ethan X
authors.initials: EX
authors.lastname: Fang
authors.affiliation: Division of Brain Injury Outcomes, Johns Hopkins Medical Institutions, 1550 Orleans Street, Baltimore, Maryland 21231, USA.
authors.forename: Daniel F
authors.initials: DF
authors.lastname: Hanley
authors.affiliation: Department of Biostatistics, Johns Hopkins University, 615 NorthWolfe Street, Baltimore, Maryland 21205, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Rosenblum
mesh_terms: D002543:Cerebral Hemorrhage / Q000628:therapy; D017322:Clinical Trials, Phase II as Topic / Q000592:standards; D006801:Humans; D017063:Outcome Assessment, Health Care / Q000379:methods* / Q000592:standards*; D016032:Randomized Controlled Trials as Topic / Q000592:standards*
keywords: Non-identifiable parameter; Randomized trial; Treatment effect heterogeneity