Analyzing multiple end points with a two-stage design in clinical trials

In many clinical trials, the assessment of the response to interventions can include a large variety of outcome variables which are generally correlated. The use of multiple significance tests is likely to increase the chance of detecting a difference in at least one of the outcomes between two treatments. Furthermore, univariate tests do not take into account the correlation structure. A new test is proposed that uses information from the interim analysis in a two-stage design to form the rejection region boundaries at the second stage. Initially, the test uses Hotelling’s T² at the end of the first stage allowing only, for early acceptance of the null hypothesis and an O’Brien ‘type’ procedure at the end of the second stage. This test allows one to ‘cheat’ and look at the data at the interim analysis to form rejection regions at the second stage, provided one uses the correct distribution of the final test statistic. This distribution is derived and the power of the new test is compared to the power of three common procedures for testing multiple outcomes: Bonferroni’s inequality, Hotelling’s T²and O’Brien’s test. O’Brien’s test has the best power to detect a difference when the outcomes are thought to be affected in exactly the same direction and the same magnitude or in exactly the same relative effects as those proposed prior to data collection. However, the statistic is not robust to deviations in the alternative parameters proposed a priori, especially for correlated outcomes. The proposed new statistic and the derivation of its distribution allows investigators to consider information from the first stage of a two-stage design and consequently base the final test on the direction observed at the first stage or modify the statistic if the direction differs significantly from what was expected a prior.