Test for qualitative interaction of clinical significance

We generalize the problem of detecting qualitative interaction between treatments and subsets in a two treatment clinical trial to the more practical problem of detecting a qualitative interaction greater than a non-negative value d, corresponding to the minimal treatment difference of clinical significance. We develop a test based on simultaneous confidence intervals for the generalized problem under the assumption of normality. The proposed test is easy to implement, either by hand calculation or through the use of virtually any existing statistical software. We derive explicit power function for the proposed test and give examples to illustrate the procedures.