Interaction tests with covariate-adaptive randomization

Treatment-covariate interaction tests are commonly applied by researchers to examine whether the treatment effect varies across patient subgroups defined by baseline characteristics. The objective of this study is to explore treatment-covariate interaction tests involving covariate-adaptive randomization. Without assuming a parametric data generation model, we investigate usual interaction tests and observe that they tend to be conservative: specifically, their limiting rejection probabilities under the null hypothesis do not exceed the nominal level and are typically strictly lower than it. To address this problem, we propose modifications to the usual tests to obtain corresponding exact tests. Moreover, we introduce a novel class of stratified-adjusted interaction tests that are simple, broadly applicable, and more powerful than the usual and modified tests. Our findings are relevant to two types of interaction tests: one involving stratification covariates and the other involving additional covariates that are not used for randomization.