Individual treatment effects in randomized trials with binary outcomes

Abstract

A potential outcomes framework is used to define individual treatment effects in a randomized design comparing two treatments, T and C. When the outcome variable is binary, individual effects may take on one of three values, 0, 1, −1, at any given point in time, but these “individual effects” cannot be measured in practice. Often, in clinical trials, an average effect of the treatment is estimated and a superior treatment is determined from this estimate. However, there may be a proportion of the population that responds favorably to T and another proportion that responds more favorably to C if individual treatment effects vary widely in the population. These proportions are nonidentifiable using data from a two sample completely randomized design, but knowledge regarding their potential magnitude is crucial for assessing the risk involved in administering a treatment to an individual. We produce identifiable bounds for these proportions using data from an unmatched 2×2 table and then demonstrate the advantages to matching in a matched-pairs design. The advantages hinge on the quality of the matching criteria. We present an extended matched-pairs design that allows estimation of refined bounds. A constructed data example is used to compare the information about individual treatment heterogeneity, and its consequences, that can be gleaned from the different designs.