Power and sample size calculations for comparison of two regression lines with heterogeneous variances

Abstract

The existence of interactive effects of a dichotomous treatment variable on the relationship between the continuous predictor and response variables is an essential issue in biological and medical sciences. Also, considerable attention has been devoted to raising awareness of the often-untenable assumption of homogeneous error variance among treatment groups. Although the procedures for detecting interactions between treatment and predictor variables are well documented in the literature, the corresponding problem of power and sample size calculations has received relatively little attention. In order to facilitate interaction design planning, this article describes power and sample size procedures for the extended Welch test of difference between two regression slopes under heterogeneity of variance. Two different formulations are presented to explicate the implications of appropriate reliance on the predictor variables. The simplified method only utilizes the partial information of predictor variances and has the advantages of statistical and computational simplifications. However, extensive numerical investigations showed that it is relatively less accurate than the more profound procedure that accommodates the full distributional features of the predictors. According to the analytic justification and empirical performance, the proposed approach gives reliable solutions to power assessment and sample size determination in the detection of interaction effects. A numerical example involving kidney weigh and body weigh of crossbred diabetic and normal mice is used to illustrate the suggested procedures with flexible allocation schemes. Moreover, the organ and body weights data is incorporated in the accompany SAS and R software programs to illustrate the ease and convenience of the proposed techniques for design planning in interactive research.