| Abstract: | The problem of investigating qualitative interactions (QI's) between subsets of patients defined by means of some risk factors, and treatment effects in clinical trials is considered from a viewpoint which leads to interchanging the hypotheses of the testing problem dealed with in the existing literature on QI's. A natural way of approaching this reverse problem is to apply one of the tests available for the original problem of detecting QI's at level 1 — α and to reject the null hypothesis of the new problem if and only if this test accepts. Unfortunately, this would require unbiasedness of the level 1 — α test for existence of QI's to start with, a property which exhibits neither the likelihood ratio procedure derived in the seminal paper of GAIL and SIMON (1985), nor the test based on the extreme order statistics which was introduced by several authors in 1993. Nevertheless we show that there is a valid test for absence of QI's which depends on the extreme values only and coincides with the maximum likelihood ratio procedure for the same problem. Furthermore, the procedure is generalized to the problem of testing for absence of relevant QI's, i.e. of qualitative interactions exceeding some specified tolerance ε > 0. |
