Detecting qualitative interactions in clinical trials: an extension of range test

To help interpret a treatment effect in clinical trials, investigators usually examine whether the observed treatment effect is the same in various subsets of patients. The qualitative interaction, which means that the treatment is beneficial in some subsets and harmful in others, is of major importance. In this paper, a new statistical test is developed for detecting such interactions. The new test is an extension of the well-known range test, but utilizes all observed treatment differences rather than only the maximum and the minimum values. Extensive simulations indicate that the proposed extended range test generally outperforms the range test and is even better than the likelihood ratio test in the sense that the extended range test is much more powerful than the likelihood test when one treatment is superior to the other in most subsets and yet does not lose much power otherwise. It is also illustrated through a real clinical trial example that the extended range test detects the qualitative interaction while the range test and likelihood ratio test do not.