ABSTRACT
The topic of multiplicity raises naturally when there are multiple endpoints in a clinical trial. Sometimes endpoints can be ranked: the hypothesis of a lower-ranking endpoint will not be rejected without rejecting all the hypotheses from higher-ranking endpoints. Sometimes endpoints do not have an obvious ranking: then it is important to determine if an inference require all of the endpoint hypotheses be rejected, or if rejecting any one of the hypotheses or a composite endpoint would be sufficient to make the inference. Different multiple comparison procedures might be suited in different scenarios. Complex multiple comparison procedures will be needed when there is a second source of multiplicity, for example, when multiple doses are evaluated or when there are multiple interim analyses for a trial with multiple endpoints. The logical and operational restriction plays an important role in determine how multiplicity adjustment is required. Details of these considerations will be reviewed in this chapter, covering the basic introduction on different types of multiple endpoints, special focus on co-primary endpoints, and considerations for multiple endpoints with another source of multiplicity.
