Analyzing Multiple Endpoints

CLAUDINE LEGAULT. Analyzing Multiple Endpoints with a two-stage group sequential design in clinical trials. (Under the direction of Timothy M. Morgan.) In many clinical trials, the assessment of the response to the various treatments can include a large variety of outcome variables which are generally correlated. Different endpoints may be regarded by the investigators as important in determining if a certain treatment is effective. The more variables there are, the more likely it is that differences will appear at random if adjustments are not made for the multiple tests. Bonferroni's adjustment for multiple comparisons is one of the approaches used when multiple correlated outcomes are being compared. For alternative hypotheses in which several endpoints are affected in the same direction, Bonferroni's procedure may lack power because the rejection of the overall hypothesis is based on the smallest pvalue of all the test. statistics. Hotelling's T 2 makes no distinction between variables that change favorably and variables that change unfavorably. It lacks power to detect any specific types of departure considered a priori to be biologically plausible in a clinical trial and was therefore considered unsuitable by Pocock (1987) for the analysis of clinical trials. A test proposed by O'Brien (1984) focusses on alternative hypotheses with all endpoints showing an effect in the same direction. In that situation it provides better power but it deteriorates sharply to a power of only 5% when variables are affected in opposite directions. This dissertation first compares the critical regions and the power contours of the three procedures mentioned above. The efficiency and robustness of these procedures are compared as a function of the direction of the alternative hypotheses. A new test is first derived using data from the interim look in a two-stage group sequential design to form the rejection boundary at the second stage. Initially, the test uses an Hotelling T 2 rejection region at the end of the first stage and an O'Brien 'type' procedure at the end of the second stage. The test is then extended to allow for early acceptance. The distribution of the proposed tests is presented and their power and efficiency are compared to common procedures. Finally, two examples are presented and future research recommendations are discussed.