Individual Treatment Effects in Randomized Trials with Binary Outcomes


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.


Mathematics and Statistics

Keywords and Phrases

Potential Response; Subject-Treatment Interaction; Clinical Trials; Contingency Tables

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2004 Elsevier, All rights reserved.

Publication Date

01 Jan 2004