Constructing a confidence interval for the fraction who benefit from treatment, using randomized trial data

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Medical Informatics

Background:

• Estimating treatment benefit, defined as the proportion of patients with better outcomes under treatment versus control, is crucial but statistically challenging.
• This parameter is only partially identifiable, even in randomized controlled trials, complicating accurate inference.
• Existing methods for confidence intervals of treatment benefit often rely on strong distributional assumptions or lack efficiency.

Purpose of the Study:

• To propose a novel, robust method for constructing confidence intervals for the fraction of patients benefiting from treatment.
• To develop a procedure that is consistent and does not necessitate assumptions on the joint distribution of potential outcomes.
• To provide a computationally efficient method applicable to binary or ordinal outcomes in clinical trials.

Main Methods:

• Development of a new confidence interval procedure based on a second-order, asymptotic approximation.
• Utilizing a stochastic optimization technique, leading to statistics that are solutions to quadratic programs.
• The method is flexible, allowing incorporation of user-defined assumptions about potential outcomes.

Main Results:

• The proposed confidence interval procedure is pointwise consistent.
• Simulations demonstrate that the method achieves nominal coverage probability or higher.
• The new method can result in narrower average confidence interval widths compared to existing approaches.

Conclusions:

• The novel method provides a reliable and efficient tool for inferring treatment benefit in randomized trials with binary or ordinal outcomes.
• Its computational efficiency, derived from quadratic programming solutions, facilitates practical application in biomedical research.
• The method was successfully applied to a clinical trial evaluating a new stroke intervention, demonstrating its real-world utility.