An expected power approach for the assessment of composite endpoints and their components

Composite endpoints are increasingly used in clinical trials, particularly in the field of cardiology. Thereby, the overall impact of the therapeutic intervention is captured by including several events of interest in a single variable. To demonstrate the significance of an overall clinical benefit, it is sufficient to assess the test problem for the composite. However, even if a statistically significant and clinically relevant superiority is shown for the composite endpoint, there is the need to evaluate the treatment effects for the components as, for example, a strong effect in one endpoint can mask an adverse effect in another. In most clinical applications, a descriptive analysis of the individual components is performed. However, the question remains what conclusion should be drawn from a trial where the composite shows a significant effect, but some component results which are not based on confirmatory evidence point in an adverse direction. Therefore, the first aim is to define an adequate multiple test problem of the composite and its most important components. Thereby, it might suffice to show superiority with respect to the composite and non-inferiority for the components to guarantee the clinical relevance of the result, as a slightly negative effect in one component might be acceptable as long as the total effect of all components is highly positive. To calculate the power for this multiple test problem, a number of strong assumptions on the effect sizes for the composite and its components as well as on the correlations between them are required. However, knowledge on these quantities is usually very limited and thus the choice of fixed parameter assumptions is based on a low level of evidence. The second aim therefore is to provide a more flexible power definition which takes the uncertainty about parameter assumptions into account. An expected power approach is proposed using prior distributions for the involved parameters. Thereby, the choice of the prior distribution reflects the level of evidence on the parameters. The expected power is evaluated for a range of scenarios and compared to the classical power for a fixed parameter setting. The new method is illustrated with a clinical trial example.