On tests of treatment-covariate interactions: An illustration of appropriate power and sample size calculations

The appraisals of treatment-covariate interaction have theoretical and substantial implications in all scientific fields. Methodologically, the detection of interaction between categorical treatment levels and continuous covariate variables is analogous to the homogeneity of regression slopes test in the context of ANCOVA. A fundamental assumption of ANCOVA is that the regression slopes associating the response variable with the covariate variable are presumed constant across treatment groups. The validity of homogeneous regression slopes accordingly is the most essential concern in traditional ANCOVA and inevitably determines the practical usefulness of research findings. In view of the limited results in current literature, this article aims to present power and sample size procedures for tests of heterogeneity between two regression slopes with particular emphasis on the stochastic feature of covariate variables. Theoretical implications and numerical investigations are presented to explicate the utility and advantage for accommodating covariate properties. The exact approach has the distinct feature of accommodating the full distributional properties of normal covariates whereas the simplified approximate methods only utilize the partial information of covariate variances. According to the overall accuracy and robustness, the exact approach is recommended over the approximate methods as a reliable tool in practical applications. The suggested power and sample size calculations can be implemented with the supplemental SAS and R programs.