Background: Binary composite outcome measures are increasingly used as primary endpoints in clinical trials. Composite endpoints combine several events of interest within a single variable. However, as the effect observed for the composite does not necessarily reflect the effects for the individual components, it is recommended in the literature to additionally evaluate each component separately.
Objectives: The task is to define an adequate multiple test procedure which focuses on the composite outcome measure but allows for a confirmatory interpretation of the components in case of large effects.
Methods: In this paper, we determine the correlation matrix for a multiple binary endpoint problem of a composite endpoint and its components based on the normal approximation test statistic for rates. Thereby, we assume multinomial distributed components. We use this correlation to calculate the adjusted local significance levels. We discuss how to use our approach for a more informative formulation of the test problem. Our work is illustrated by two clinical trial examples.
Results: By taking into account the special correlation structure between a binary composite outcome and its components, an adequate multiple test procedure to assess the composite and its components can be defined based on an approximate multivariate normal distribution without much loss in power compared to a test problem formulated exclusively for the composite.
Conclusions: By incorporating the correlation under the null hypotheses, the global power for the multiple test problem assessing both the composite and its components can be increased as compared to simple Bonferroni-adjustment. Thus, a confirmatory analysis of the composite and its components might be possible without a large increase in sample size as compared to a single endpoint problem formulated exclusively for the composite.