  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 generating 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 valid tests. Moreover, we introduce a novel class
of stratified-adjusted interaction tests that are simple, more powerful than
the usual and modified tests, and broadly applicable to most covariate-adaptive
randomization methods. The results are general to encompass two types of
interaction tests: one involving stratification covariates and the other
involving additional covariates that are not used for randomization. Our study
clarifies the application of interaction tests in clinical trials and offers
valuable tools for revealing treatment heterogeneity, crucial for advancing
personalized medicine.
