title: Understanding Variation in Sets of N-of-1 Trials.
abstract: A recent paper in this journal by Chen and Chen has used computer simulations to examine a number of approaches to analysing sets of n-of-1 trials. We have examined such designs using a more theoretical approach based on considering the purpose of analysis and the structure as regards randomisation that the design uses. We show that different purposes require different analyses and that these in turn may produce quite different results. Our approach to incorporating the randomisation employed when the purpose is to test a null hypothesis of strict equality of the treatment makes use of Nelder's theory of general balance. However, where the purpose is to make inferences about the effects for individual patients, we show that a mixed model is needed. There are strong parallels to the difference between fixed and random effects meta-analyses and these are discussed.
authors.affiliation: Competence Center for Methodology and Statistics, Luxembourg Institute of Health, Strassen, Luxembourg.
authors.forename: Artur
authors.initials: A
authors.lastname: Araujo
authors.affiliation: Medical Statistics Group, School of Health and Related Research, University of Sheffield, Sheffield, United Kingdom.
authors.forename: Steven
authors.initials: S
authors.lastname: Julious
authors.affiliation: Competence Center for Methodology and Statistics, Luxembourg Institute of Health, Strassen, Luxembourg.
authors.forename: Stephen
authors.identifier: http://orcid.org/0000-0002-7558-8473
authors.initials: S
authors.lastname: Senn
mesh_terms: D000465:Algorithms; D035843:Biomedical Research / Q000379:methods / Q000706:statistics & numerical data; D002986:Clinical Trials as Topic; D006801:Humans; D015233:Models, Statistical; D012107:Research Design