title: Power and sample size for clinical trials when efficacy is required in multiple endpoints: application to an Alzheimer's treatment trial.
abstract: BACKGROUND
  When the efficacy of a treatment in a randomized controlled trial is required for multiple primary endpoints, trial design and analysis differ from trial requiring efficacy in only one of the multiple endpoints.
  
  
  METHODS
  We consider a two-arm clinical trial requiring efficacy analysis for multiple primary endpoints, formulating the appropriate null and alternative hypotheses for the test of treatment efficacy. We study the significance level/statistical power of an intersection-union test (IUT) in this situation. We compare IUT with the intuitive approach (selecting the maximum sample size over those obtained from testing individual primary endpoints one by one) for determination of sample size.
  
  
  RESULTS
  The proposed IUT reserves the same Type I error rate as shared by all endpoint-specific tests. The statistical power of the proposed IUT is no more than the minimum from the individual tests. The maximum sample size from multiple endpoint-specific tests is often inadequate for the test of treatment efficacy, especially when the standardized effect sizes are similar. Finally, the IUT can be applied to Alzheimer's disease treatment trials in which two primary endpoints are typically used.
  
  
  CONCLUSIONS
  The IUT is a valid method for use in the design and analysis of clinical trials requiring efficacy at multiple primary endpoints.
authors.affiliation: Division of Biostatistics, Washington University in St Louis, MO 63110, USA. chengjie@wubios.wustl.edu
authors.forename: Chengjie
authors.initials: C
authors.lastname: Xiong
authors.forename: Kai
authors.initials: K
authors.lastname: Yu
authors.forename: Feng
authors.initials: F
authors.lastname: Gao
authors.forename: Yan
authors.initials: Y
authors.lastname: Yan
authors.forename: Zhengjun
authors.initials: Z
authors.lastname: Zhang
mesh_terms: D000544:Alzheimer Disease / Q000628:therapy; D002986:Clinical Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D006801:Humans; D012107:Research Design; D018401:Sample Size; D016896:Treatment Outcome