A comparison of the power of two tests for qualitative interactions

‘Qualitative’ or ‘crossover’ interactions arise when a new treatment, compared with a control treatment, is beneficial in some subsets of patients and harmful in other subsets. We present a new range test for crossover interactions and compare it with the likelihood ratio test developed by Gail and Simon. The range test has greater power when the new treatment is harmful in only a few subsets, whereas the likelihood ratio test has greater power when the new treatment is harmful in several subsets. We provide power tables for both tests to facilitate sample size calculations for designing experiments to detect qualitative interactions and for interpreting the results of clinical trials.