Power and sample size procedures for equivalence assessment of treatment-covariate interactions and simple effects under variance heterogeneity: An emphasis on random covariates

Abstract The renowned Welch procedures are useful for comparing treatment means in two-sample designs and slope coefficients in linear regressions when the homogenous variances assumption is not tenable. The Welch-type two one-sided tests (TOST) procedure has been proposed to assess the similarity and comparability between two treatment means. The technical simplicity facilitates a direct analog extension of the heteroscedastic TOST procedure for testing slope equivalence under variance heterogeneity. This paper presents the associated power function that accommodates the distributional properties of normal covariates. Moreover, the investigation extends to the equivalence appraisal of simple effects or the difference of mean responses at a focal covariate value. Numerical examinations are conducted to justify the advantage of the proposed power function over the existing method, which fails to account for the random features of covariate variables. The recommended power and sample size calculations expedite design planning and the overall utility of heteroscedastic TOST procedures for equivalence analysis in practical application.