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This book integrates recent methodological developments for calculating the sample size and power in trials with more than one endpoint considered as multiple primary or co-primary, offering an important reference work for statisticians working in this area.

The determination of sample size and the evaluation of power are fundamental and critical elements in the design of clinical trials. If the sample size is too small, important effects may go unnoticed; if the sample size is too large, it represents a waste of resources and unethically puts more participants at risk than necessary. Recently many clinical trials have been designed with more than one endpoint considered as multiple primary or co-primary, creating a need for new approaches to the design and analysis of these clinical trials. The book focuses on the evaluation of power and sample size determination when comparing the effects of two interventions in superiority clinical trials with multiple endpoints. Methods for sample size calculation in clinical trials where the alternative hypothesis is that there are effects on ALL endpoints are discussed in detail. The book also briey examines trials designed with an alternative hypothesis of an effect on AT LEAST ONE endpoint with a prespecified non-ordering of endpoints.

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1.Introduction.- 2.Continuous Co-primary Endpoints.- 3.Binary Co-primary Endpoints.- 4.Convenient Sample Size Formula.- 5.Continuous Primary Endpoints.- 6. Further Developments.- A.Sample Size Calculation Using other Contrasts for Binary Endpoints.- B.Empirical Power for Sample Size Calculation for Binary Co-primary Endpoints.- C.Numerical Tables for Ck in the Convenient Sample Size Formula for the Three Co-primary Continuous Endpoints Cace.- D.Software Programs for Sample Size Calculation for Continuous Co-primary Endpoints.- References.

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Takashi Sozu

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