Unit-treatment interaction and its practical consequences

Most statistical characterizations of a treatment effect focus on the avera ge effect of the treatment over an entire population. However, average effe cts: may provide inadequate information, sometimes misleading information, when a substantial unit-treatment interaction is present in the population. It is even possible that a nonnegligible proportion of the individuals in the population experience an unfavorable treatment effect even though the t reatment might appear to be beneficial when considering population averages . This paper examines the extent to which information about unit-treatment interaction can be extracted using observed data from a two-treatment compl etely randomized experiment. A method for utilizing the information from an available covariate is proposed. Although unit-treatment interaction is a nonidentifiable quantity, we show that mathematical bounds for it can be es timated from observed data. These bounds lead to estimated bounds for the p robability of an unfavorable treatment effect. Maximum likelihood estimator s of the bounds and their corresponding large-sample distributions are give n. The use of the estimated bounds is illustrated in a clinical trials data example.