Statistical planning to address strongly correlated endpoints for inferential subgroups: An innovative approach for an illustrative clinical trial with complex multiplicity issues

Multiplicity is an important statistical issue that arises in clinical trials when the efficacy of the test treatment is evaluated in multiple ways. The major concern for multiplicity is that uncontrolled multiple assessments lead to inflated family-wise Type I error, and they thereby undermine the integrity of the statistical inferences. Multiplicity comes from different sources, for example, making inferences either on the overall population or some pre-specified sub-populations, while multiple endpoints need to be evaluated for each population. Therefore, a sound statistical strategy that controls the family-wise Type I error rate in a strong sense, without excessive loss of power from over-control, is crucial for the success of the trial. For a recent phase III cardiovascular trial with such complex multiplicity, we illustrate the use of a closed testing strategy that begins with a global test; and subsequent testing only proceeds when the global test is rejected. Also, we discuss a simulation study based on this trial to compare the power of the illustrated closed testing strategy to some well-known alternative approaches. We found that this strategy can comprehensively meet most of the primary objectives of the trial effectively with reasonably high overall power.