Permutation Testing for Treatment-Covariate Interactions and Subgroup Identification

We consider the problem of using permutation-based methods to test for treatment-covariate interactions from randomized clinical trial data. Testing for interactions is common in the field of personalized medicine, as subgroups with enhanced treatment effects arise when treatment-by-covariate interactions exist. Asymptotic tests can often be performed for simple models, but in many cases, more complex methods are used to identify subgroups, and non-standard test statistics proposed, and asymptotic results may be difficult to obtain. In such cases, it is natural to consider permutation-based tests, which shuffle selected parts of the data in order to remove one or more associations of interest; however, in the case of interactions, it is generally not possible to remove only the associations of interest by simple permutations of the data. We propose a number of alternative permutation-based methods, designed to remove only the associations of interest, but preserving other associations. These methods estimate the interaction term in a model, then create data that "looks like" the original data except that the interaction term has been permuted. The proposed methods are shown to outperform traditional permutation methods in a simulation study. In addition, the proposed methods are illustrated using data from a randomized clinical trial of patients with hypertension.