Individual treatment effects in randomized trials with binary outcomes

• Published in: Journal of statistical planning and inference Vol. 121; no. 2; pp. 163 - 174
• Main Authors: Gadbury, Gary L., Iyer, Hari K., Albert, Jeffrey M.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.04.2004; New York,NY Elsevier Science; Amsterdam
• Subjects: Applications; Biology, psychology, social sciences; Clinical trials; Contingency tables; Exact sciences and technology; Experimental design; Mathematics; Medical sciences; Potential response; Probability and statistics; Sciences and techniques of general use; Statistics; Subject-treatment interaction; Subject-treatment interaction; 62P10; 62A01; Clinical trials; Potential response; 62K99; Contingency tables; Biometrics; Statistical method; Heterogeneity; Medical science; Matched sample; Randomized design; Treatment effect; Binary response; Clinical trial; Statistical decision; Mean estimation
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(03)00115-0

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.