title: Design, analysis and presentation of factorial randomised controlled trials.
abstract: BACKGROUND
  The evaluation of more than one intervention in the same randomised controlled trial can be achieved using a parallel group design. However this requires increased sample size and can be inefficient, especially if there is also interest in considering combinations of the interventions. An alternative may be a factorial trial, where for two interventions participants are allocated to receive neither intervention, one or the other, or both. Factorial trials require special considerations, however, particularly at the design and analysis stages.
  
  
  CONCLUSIONS
  Using a 2 x 2 factorial trial as an example, we present a number of issues that should be considered when planning a factorial trial. The main design issue is that of sample size. Factorial trials are most often powered to detect the main effects of interventions, since adequate power to detect plausible interactions requires greatly increased sample sizes. The main analytical issues relate to the investigation of main effects and the interaction between the interventions in appropriate regression models. Presentation of results should reflect the analytical strategy with an emphasis on the principal research questions. We also give an example of how baseline and follow-up data should be presented. Lastly, we discuss the implications of the design, analytical and presentational issues covered.
  
  
  CONCLUSIONS
  Difficulties in interpreting the results of factorial trials if an influential interaction is observed is the cost of the potential for efficient, simultaneous consideration of two or more interventions. Factorial trials can in principle be designed to have adequate power to detect realistic interactions, and in any case they are the only design that allows such effects to be investigated.
authors: Division of Primary Health Care, University of Bristol, Cotham House, Cotham Hill, Bristol BS6 6JL, UK. alan.a.montgomery@bristol.ac.uk
authors: Alan A
authors: AA
authors: Montgomery
authors: Tim J
authors: TJ
authors: Peters
authors: Paul
authors: P
authors: Little
mesh_terms: D003627:Data Interpretation, Statistical; D006801:Humans; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D012107:Research Design; D018401:Sample Size