title: Reducing sample size by combining superiority and non-inferiority for two primary endpoints in the Social Fitness study.
abstract: In randomized controlled trials, two endpoints may be necessary to capture the multidimensional concept of the intervention and the objectives of the study adequately. We show how to calculate sample size when defining success of a trial by combinations of superiority and/or non-inferiority aims for the endpoints.
  
  
  
  The randomized controlled trial design of the Social Fitness study uses two primary endpoints, which can be combined into five different scenarios for defining success of the trial. We show how to calculate power and sample size for each scenario and compare these for different settings of power of each endpoint and correlation between them.
  
  
  
  Compared to a single primary endpoint, using two primary endpoints often gives more power when success is defined as: improvement in one of the two endpoints and no deterioration in the other. This also gives better power than when success is defined as: improvement in one prespecified endpoint and no deterioration in the remaining endpoint.
  
  
  
  When two primary endpoints are equally important, but a positive effect in both simultaneously is not per se required, the objective of having one superior and the other (at least) non-inferior could make sense and reduce sample size.
authors.affiliation: Scientific Center for Quality of Healthcare, Radboud Institute for Health Sciences, Radboud University Medical Center, 114 IQ healthcare P.O. Box 9101, 6500 HB Nijmegen, The Netherlands; Radboudumc Alzheimer Center, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, RAC 925, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands. Electronic address: Hanneke.Donkers@radboudumc.nl.
authors.forename: Hanneke
authors.initials: H
authors.lastname: Donkers
authors.affiliation: Scientific Center for Quality of Healthcare, Radboud Institute for Health Sciences, Radboud University Medical Center, 114 IQ healthcare P.O. Box 9101, 6500 HB Nijmegen, The Netherlands; Radboudumc Alzheimer Center, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, RAC 925, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands; Department of Rehabilitation, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, 898, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands.
authors.forename: Maud
authors.initials: M
authors.lastname: Graff
authors.affiliation: Scientific Center for Quality of Healthcare, Radboud Institute for Health Sciences, Radboud University Medical Center, 114 IQ healthcare P.O. Box 9101, 6500 HB Nijmegen, The Netherlands; Radboudumc Alzheimer Center, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, RAC 925, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands.
authors.forename: Myrra
authors.initials: M
authors.lastname: Vernooij-Dassen
authors.affiliation: Scientific Center for Quality of Healthcare, Radboud Institute for Health Sciences, Radboud University Medical Center, 114 IQ healthcare P.O. Box 9101, 6500 HB Nijmegen, The Netherlands; Department of Rehabilitation, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, 898, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands.
authors.forename: Maria
authors.initials: M
authors.lastname: Nijhuis-van der Sanden
authors.affiliation: Section Biostatistics, Department for Health Evidence, Radboud Institute for Health Sciences, Radboud University Medical Center, 133 HEV, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands.
authors.forename: Steven
authors.initials: S
authors.lastname: Teerenstra
mesh_terms: D002170:Canada; D023381:Endpoint Determination / Q000379:methods* / Q000706:statistics & numerical data; D015340:Epidemiologic Research Design; D006801:Humans; D010549:Personal Satisfaction; D018401:Sample Size; D012919:Social Behavior
keywords: COPM; Cluster randomized trial; Combined objectives; Non-inferiority; Sample size; Superiority