Detecting treatment-covariate interactions using permutation methods.

The primary objective of a Randomized Clinical Trial usually is to investigate whether one treatment is better than its alternatives on average. However, treatment effects may vary across different patient subpopulations. In contrast to demonstrating one treatment is superior to another on the average sense, one is often more concerned with the question that, for a particular patient, or a group of patients with similar characteristics, which treatment strategy is most appropriate to achieve a desired outcome. Various interaction tests have been proposed to detect treatment effect heterogeneity; however, they typically examine covariates one at a time, do not offer an integrated approach that incorporates all available information, and can greatly increase the chance of a false positive finding when the number of covariates is large. We propose a new permutation test for the null hypothesis of no interaction effects for any covariate. The proposed test allows us to consider the interaction effects of many covariates simultaneously without having to group subjects into subsets based on pre-specified criteria and applies generally to randomized clinical trials of multiple treatments. The test provides an attractive alternative to the standard likelihood ratio test, especially when the number of covariates is large. We illustrate the proposed methods using a dataset from the Treatment of Adolescents with Depression Study.