A test for the difference between two treatments in a continuous measure of outcome when there are dropouts

Consider a randomized clinical trial that is designed to compare two treatments in which the treatment continues during the entire period of the study. Some subjects may refuse to complete the protocol and will not return for the final evaluation. Since the reason for dropping out may be related to the subject's self-assessed evaluation of the usefulness of the treatment or to undesirable side effects of the treatment, subjects who drop out cannot be treated as a random sample of those who entered the trial. We consider the situation where the measure of efficacy of the treatment is continuous. Under the assumption that the expected value of the measure for those who drop out is not better (the direction depends on the measure) than that for those who complete the study, we propose an adjustment to the usual test for a difference between treatments that allows for the inclusion of the probable effect of the dropouts; this provides a bound on the test for efficacy of the treatment. First, we estimate a predetermined percentile, such as the median score, of the control, or placebo, group and assign this score to all those who dropped out from both groups and to all subjects in both groups with scores that are worse than the assigned score. A Mann-Whitney statistic is then used to test the equality of the distributions of the two groups. We show by simulation that this modified test is equivalent to a test using the complete data and has greater power than that obtained when including the dropouts by assigning the worst observed score to them. This test will be less sensitive to bias that is induced by exclusion of dropouts from the final evaluation.