In clinical trials, the efficacy of treatment might be dependent on the value of a covariate variable. Therefore, it might be possible to detect the region over the covariate variable where the two treatments under investigation do not have significantly different efficacy or the region of superiority of one treatment. The non-significant region can be verified to be a confidence interval for the abscissa of the intersection point of two regression lines, and each of the complementary regions of the confidence interval corresponds to a region of superiority. In this study, we develop a method of constructing the confidence interval based on the concept of a generalized pivotal quantity, so as to perform the task of detecting the possible three regions for a clinical trial. Two real-world examples are given to illustrate the application of our proposed method, and a simulation study is conducted to evaluate its performance.
Keywords: Analysis of covariance analysis; Johnson-Neyman procedure; clinical trial; generalized pivotal quantity; regression analysis.