Aberrant Effects of Treatment

Often, the protocol for a randomized controlled trial states that if a patient’s health deteriorates substantially in certain specific ways, then the study treatments will no longer be considered adequate medical care, and the patient will be taken off the study treatments and given the needed care. Aberrant responses of this sort present special problems of interpretation. The few such patients may have received only limited exposure to the study treatments, but also may have experienced some of the worst outcomes observed in the trial. The most basic question is whether one of the treatments tends to cause such aberrant responses, quite apart from any other beneficial or harmful effects that treatment may have. Common practice is to reduce aberrant responses to binary events and apply Fisher’s exact test for a 2×2 table, but this approach discards the available information about the magnitude of the aberration. We propose a new randomization test for this problem that uses information about both the number of aberrations and their magnitude. In extreme situations, the new test reduces to either Fisher’s exact test or Wilcoxon’s rank sum test, but in common situations, the new test has features of both methods. Importantly, this exact test reacts only to aberrant effects; it is completely unaffected by treatment effects that do not produce aberrations. When aberrant responses have several aspects, we examine the consequences of selecting, after the fact, the one aspect exhibiting the greatest aberration, and applying the test to that aspect. For a single response variable, a confidence interval is proposed for an additive aberrant effect; the interval is constructed by inverting the test, and a multivariate extension is briefly mentioned. We illustrate the use of the test in the ACE-Inhibitor After Anthracycline (AAA) randomized trial, which was aimed at preserving cardiac function in children treated for cancer. Seven of 135 children were removed from the trial due to substantial cardiac declines; 6 of these were on placebo, 1 of whom subsequently died.