Incorporating the sample correlation into the testing of two endpoints in clinical trials.

We introduce an improved Bonferroni method for testing two primary endpoints in clinical trial settings using a new data-adaptive critical value that explicitly incorporates the sample correlation coefficient. Our methodology is developed for the usual Student's t-test statistics for testing the means under normal distributional setting with unknown population correlation and variances. Specifically, we construct a confidence interval for the unknown population correlation and show that the estimated type-1 error rate of the Bonferroni method with the population correlation being estimated by its lower confidence limit can be bounded from above less conservatively than using the traditional Bonferroni upper bound. We also compare the new procedure with other procedures commonly used for the multiple testing problem addressed in this paper.