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A variety of weighted effect measures and analysis approaches for composite endpoints were proposed in the literature of which most refer to time-to-event composite endpoints (Lachin and Bebu, Clin Trials 12:627–633, 2015; Bakal et al., Stat Methods Med Res 24:980–988, 2015; Bakal et al., Eur Heart J 34:903–908, 2013; Pocock et al., Eur Heart J 33:176–182, 2012; Buyse, Stat Med 29:3245–3257, 2010; Hallstrom et al., Control Clin Trials 13:148–155, 1992). Similar as for composite binary endpoints, application of most methods should be done with care as will be explored in more detail in Chap. 14, compare also Bebu and Lachin (2016) and Rauch et al. (2014). In this chapter, we introduce a weighted effect measure and a related test as proposed by Rauch et al. (2016, to be published). The common effect measure for composite time-to-event endpoints is the all-cause hazard ratio which gives equal weight to all types of events irrespective of their clinical relevance. Thereby, the all-cause hazard within each group is given by the sum of the cause-specific hazards corresponding to the individual components. A natural extension of the standard all-cause hazard ratio can be defined by a “weighted all-cause hazard ratio” where the individual hazards for each component are multiplied with predefined relevance weighting factors. For the special case of equal weights across the components, the weighted all-cause hazard ratio then corresponds to the standard all-cause hazard ratio. In this chapter, the weighted all-cause hazard ratio will be introduced as a new weighted effect measure. Moreover, a related statistical test will be proposed.

In clinical trials, the primary efficacy variable often corresponds to a so-called composite endpoint. Such an endpoint combines information from different variables within a single net measure. The choice of a composite primary endpoint can be motivated by different considerations. In order to understand and discuss the rationale for the use of composite endpoints and the related problems, we will first start by providing an explicit definition of composite endpoints. Once the definition is clear, the rationale for the use of composite endpoints is easily deduced.

A number of other effect measures and analysis approaches for composite endpoints which take account of the different clinical relevance of the components were proposed in the literature; compare, for example, Lachin and Bebu (Clin Trials 12:627–633, 2015), Bakal et al. (Stat Methods Med Res 24:980–988, 2015), Bakal et al. (Eur Heart J 34:903–908, 2013), Pocock et al. (Eur Heart J 33:176–182, 2012), Buyse (Stat Med 29:3245–3257, 2010), and Hallstrom et al. (Control Clin Trials 13:148–155, 1992). As it goes beyond the scope of this book to present a complete and systematic literature review on weighted approaches, only a few exemplary methods will be presented and discussed within this chapter. Many of the weighting approaches presented in the literature should be used and interpreted with care as they are subject to general mathematical concerns. For example, unlike the weighting approaches presented in the previous chapters, many of the approaches proposed in the literature combine first and subsequent events irrespective of their underlying correlation structure and irrespective of the competing risk situation. Moreover, most of these approaches ignore the observational period making the approaches sensitive to changes in the follow-up distribution. Therefore, we generally recommend to apply weighted composite effect measures only when the properties of the method are really understood which usually requires a thorough mathematical look on the methodological aspects.

In the previous chapter, it has been shown that a composite endpoint can help to increase the power or save sample size and can define an alternative to a multiple endpoint test problem. Despite these favorable properties of composite endpoints, there also exist some major problems and challenges related to composite endpoints which will be outlined in the following.

The resulting treatment effect of a composite endpoint alone is often difficult to interpret as the individual components do not necessarily contribute the same amounts to this net effect. As discussed before, current guidelines therefore recommend to always analyze the components of composite endpoints separately. The current well-established practice is to provide descriptive analyses of the components and the composite in addition to the confirmatory analysis of the composite. However, there exist a number of different methods to evaluate the single components in a descriptive manner. In this chapter, the most common approaches for a descriptive analysis of the individual components will be presented and discussed. Moreover, we will deduce recommendations for a meaningful presentation and interpretation of the component-specific results.

In this chapter, several clinical trial examples will be presented which will be used in the remainder of the book to discuss different clinical trial situations in which composite endpoints might be applied and to illustrate possible planning and analysis strategies for studies with composite endpoints.

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.

As discussed above, clinical trials using a composite endpoint as primary outcome are often difficult to interpret as the single components may show varying or even opposite treatment effects. Although a descriptive analysis of the single components is the current standard and can reveal those problems, this approach does not provide any confirmatory evidence and thus gives no guidance for a definite conclusion on the treatment efficacy. Methods for a confirmatory analysis of a composite endpoint and one main component have been presented in Part III of this book. In there, the focus was to define an efficacy claim based on a multiple test problem and to calculate the sample size such that there is sufficient power to reach this claim. However, a confirmatory analysis of the components can still be of interest, even if the underlying multiple test problem does not correspond to the formal efficacy claim for which the trial is powered. In this chapter, the focus lies on simple confirmatory multiple test strategies for the components which provide a reasonable chance to get additional confirmatory evidence without the need to increase sample size.

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.

As motivated in Part I of this book, a major difficulty when planning a clinical trial with a composite primary endpoint or, as an alternative, with a single component as primary efficacy measure is to make valid planning assumptions on the required parameters and the expected effect size. A common way to deal with planning uncertainties is the use of adaptive or classical group-sequential designs, which allow an early stop of the trial either for futility or, in case of an unexpectedly large effect, also for efficacy. It is intuitively clear that the option of an early termination of the trial can decrease the total required sample size by a relevant amount. In adaptive designs, it is moreover possible to change other trial settings such as the second-stage sample size or the test strategy. As repeated hypothesis tests are performed in group-sequential and adaptive designs, the local significance levels for each individual analysis have to be adjusted in order to maintain the global type I error rate. Therefore, under the correct parameter assumptions, the maximal required sample size of such a design is larger than the sample size for a standard single-stage design.

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.

This chapter provides exemplary source code written in the software R implementing different approaches outlined in Part III of this book.

Similar to the previous chapter, we discuss in this chapter several original clinical trials for time-to-event composite endpoints along with their designs, results, and possible limitations. The focus is again 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.

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.

In the previous chapter, the challenges and problems related to composite endpoints have been outlined. A number of guidelines exist discussing composite endpoints in various contexts such as in the context of clinical trial application for drugs or medicinal products or in the context of benefit-risk assessment. It is in the nature of things that the existing guidelines are revised and new ones are developed continuously. Therefore, it is not possible to give an exhaustive overview on the perspective of guidelines related to composite endpoints. Instead, in the following some relevant guideline documents will be highlighted, and major topics related to composite endpoints addressed in these guidelines will be outlined.