Effects of Heteroscedasticity Upon Certain Analyses When Regression Lines are Not Parallel

Abstract

The two sample analysis of covariance model is considered where the regression lines are found not to be parallel. There are two analyses often utilized in this case. One is to obtain a standard confidence interval for the covariate value where the two lines intersect, and the other is to find a simultaneous confidence region for the difference between the regression lines. The asymptotic robustness to heteroscedasticity of the regressions' errors of the coverage probability of each of these two confidence procedures is considered. When the sample sizes are approximately equal, and the covariate means and the covariate variances are similar between the samples, the unequal regression variances are shown to have little effect on the asymptotic coverage probabilities of these two confidence procedures. Discussions concerning the effects of unequal sample sizes and inequitably distributed covariate values are also presented. These results are illustrated in application to a clinical trial of recombinant human erythropoetin versus placebo to treat patients with anemia secondary to advanced cancer, who were not receiving chemotherapy.