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A variety of weighted effect measures and analysis approaches for composite endpoints were proposed in the literature of which only a few are applicable to composite binary endpoints (Pocock et al., Eur Heart J 33:176–182, 2012; Buyse, Stat Med 29:3245–3257, 2010). Many of these approaches should be applied with care as explored in more detail in Chap. 14. Therefore, in this chapter, an alternative weighted effect measure for a composite binary endpoint will be introduced. As motivated above, an intuitive way to define a weighted effect measure is to extend the standard unweighted effect measure in a reasonable way. For a binary endpoint, the common effect measure is the absolute risk difference. In the remainder of this chapter, a weighted version of this risk difference will be introduced.

It is evident that the composite endpoint is, by definition, correlated to its components as every event related to a component is also an event in the composite. This correlation might be incorporated in different ways in the planning stage and/or the analysis of the trial and is hence of general interest. Therefore, in this chapter the correlations between a composite and a single component and the correlation between two individual components are deduced for binary and time-to-event endpoints.

In this chapter, the test problem is introduced for the case of a standard single-stage design, meaning that no interim analysis is performed. The underlying parameters and distributional assumptions, the test problems, and the test statistics will be separately formulated for (composite) binary endpoints and for (composite) time-to-(first-)event endpoints. Moreover, approaches to calculate the required sample size are provided.

In this chapter, we discuss several original clinical trials for composite binary endpoints along with their designs, results, and possible limitations. The focus of this chapter is to propose and apply alternative planning and analysis strategies which might help to improve the performance of the design or to ease interpretation of results.

We consider clinical trials with a binary composite endpoint where the trial is successful when a significant result is achieved for the composite or one prespecified main component. Appropriate sample size planning is challenging in this situation, as in addition to the Type I error rate, power, and target difference the overall event rates and the correlation between the test statistics have to be defined. Reliable estimates of these quantities, however, are usually hard to obtain and therefore there is a high risk to not achieve the intended power in a fixed sample size design. In this article, we propose an internal pilot study design where the nuisance parameters are estimated in a blinded way at an interim stage and where the sample size is then revised accordingly. We investigate the characteristics of the proposed design with respect to the actual Type I error rate, power, and sample size. The application of this design is illustrated by a clinical trial example.