Unit-treatment Interaction and Its Practical Consequences

Most statistical characterizations of a treatment effect focus on the average effect of the treatment over an entire population. However, average effects 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 treatment 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 completely 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 estimated from observed data. These bounds lead to estimated bounds for the probability of an unfavorable treatment effect. Maximum likelihood estimators of the bounds and their corresponding large-sample distributions are given. The use of the estimated bounds is illustrated in a clinical trials data example.