{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T15:22:19Z","timestamp":1790090539293,"version":"4.0.1"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T00:00:00Z","timestamp":1692144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"},{"start":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T00:00:00Z","timestamp":1692144000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"WISS 2025 project 'IDA-Lab Salzburg'","award":["20102-F1901166-KZP"],"award-info":[{"award-number":["20102-F1901166-KZP"]}]},{"name":"WISS 2025 project 'IDA-Lab Salzburg'","award":["20204-WISS\/225\/197-2019"],"award-info":[{"award-number":["20204-WISS\/225\/197-2019"]}]},{"name":"European Joint Programme on Rare Diseases (EJP RD), EU Horizon 2020","award":["grant agreement no. 825575"],"award-info":[{"award-number":["grant agreement no. 825575"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>To optimize the use of data from a small number of subjects in rare disease trials, an at first sight advantageous design is the repeated measures cross-over design. However, it is unclear how these within-treatment period and within-subject clustered data are best analyzed in small-sample trials. In a real-data simulation study based upon a recent epidermolysis bullosa simplex trial using this design, we compare non-parametric marginal models, generalized pairwise comparison models, GEE-type models and parametric model averaging for both repeated binary and count data. The recommendation of which methodology to use in rare disease trials with a repeated measures cross-over design depends on the type of outcome and the number of time points the treatment has an effect on. The non-parametric marginal model testing the treatment\u2013time-interaction effect is suitable for detecting between group differences in the shapes of the longitudinal profiles. For binary outcomes with the treatment effect on a single time point, the parametric model averaging method is recommended, while in the other cases the unmatched generalized pairwise comparison methodology is recommended. Both provide an easily interpretable effect size measure, and do not require exclusion of periods or subjects due to incompleteness.<\/jats:p>","DOI":"10.1111\/biom.13920","type":"journal-article","created":{"date-parts":[[2023,8,20]],"date-time":"2023-08-20T21:38:09Z","timestamp":1692567489000},"page":"3998-4011","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["How to Analyze Continuous and Discrete Repeated Measures in Small-Sample Cross-Over Trials?"],"prefix":"10.1093","volume":"79","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4923-1032","authenticated-orcid":false,"given":"Johan","family":"Verbeeck","sequence":"first","affiliation":[{"name":"Data Science Institute (DSI), Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Hasselt University , Hasselt , Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Geroldinger","sequence":"additional","affiliation":[{"name":"Team Biostatistics and Big Medical Data, Intelligent Data Analytics (IDA) Lab Salzburg, Paracelsus Medical University , Salzburg , Austria"},{"name":"Research and Innovation Management, Paracelsus Medical University Salzburg , Salzburg , Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Konstantin","family":"Thiel","sequence":"additional","affiliation":[{"name":"Team Biostatistics and Big Medical Data, Intelligent Data Analytics (IDA) Lab Salzburg, Paracelsus Medical University , Salzburg , Austria"},{"name":"Research and Innovation Management, Paracelsus Medical University Salzburg , Salzburg , Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2676-5912","authenticated-orcid":false,"given":"Andrew Craig","family":"Hooker","sequence":"additional","affiliation":[{"name":"Department of Pharmacy, Uppsala University , Uppsala , Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sebastian","family":"Ueckert","sequence":"additional","affiliation":[{"name":"Department of Pharmacy, Uppsala University , Uppsala , Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mats","family":"Karlsson","sequence":"additional","affiliation":[{"name":"Department of Pharmacy, Uppsala University , Uppsala , Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arne Cornelius","family":"Bathke","sequence":"additional","affiliation":[{"name":"Intelligent Data Analytics (IDA) Lab Salzburg, Department of Artificial Intelligence and Human Interfaces, University of Salzburg , Salzburg , Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johann Wolfgang","family":"Bauer","sequence":"additional","affiliation":[{"name":"Department of Dermatology and Allergology, Paracelsus Medical University , Salzburg , Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Geert","family":"Molenberghs","sequence":"additional","affiliation":[{"name":"Data Science Institute (DSI), Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Hasselt University , Hasselt , Belgium"},{"name":"Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), KULeuven , Leuven , Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Georg","family":"Zimmermann","sequence":"additional","affiliation":[{"name":"Team Biostatistics and Big Medical Data, Intelligent Data Analytics (IDA) Lab Salzburg, Paracelsus Medical University , Salzburg , Austria"},{"name":"Research and Innovation Management, Paracelsus Medical University Salzburg , Salzburg , Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,8,16]]},"reference":[{"key":"2024013111545919800_biom13920-bib-0001","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.3390\/math11061502","article-title":"Exact permutation and bootstrap distribution of generalized pairwise comparisons statistics","volume":"11","author":"Anderson","year":"2023","journal-title":"Mathematics"},{"key":"2024013111545919800_biom13920-bib-0002","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s10928-017-9550-0","article-title":"Model selection and averaging of nonlinear mixed-effect models for robust phase III dose selection","volume":"44","author":"Aoki","year":"2017","journal-title":"Journal of Pharmacokinetics and Pharmacodynamics"},{"key":"2024013111545919800_biom13920-bib-0003","first-page":"233","article-title":"Pseudolikelihood estimation: some examples","volume":"53","author":"Arnold","year":"1991","journal-title":"Sankhya: the Indian Journal of Statistics-Series B"},{"key":"2024013111545919800_biom13920-bib-0004","first-page":"123","article-title":"Significance tests for 2 2 tables","volume":"34","author":"Barnard","year":"1947","journal-title":"Biometrika"},{"key":"2024013111545919800_biom13920-bib-0005","first-page":"268","article-title":"Properties of sufficiency and statistical tests","volume":"160","author":"Bartlett","year":"1937","journal-title":"Proceedings of the Royal Society A"},{"key":"2024013111545919800_biom13920-bib-0006","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1016\/j.csda.2007.04.020","article-title":"A simulation study comparing weighted estimating equations with multiple imputation based estimating equations for longitudinal binary data","volume":"52","author":"Beunckens","year":"2008","journal-title":"Computational Statistics & Data Analysis"},{"key":"2024013111545919800_biom13920-bib-0007","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1111\/j.1541-0420.2005.00344.x","article-title":"Combining multiple comparisons and modeling techniques in dose\u2013response studies","volume":"61","author":"Bretz","year":"2005","journal-title":"Biometrics"},{"key":"2024013111545919800_biom13920-bib-0008","volume-title":"Nonparametric analysis of longitudinal data in factorial experiments","author":"Brunner","year":"2002"},{"key":"2024013111545919800_biom13920-bib-0009","doi-asserted-by":"crossref","first-page":"3245","DOI":"10.1002\/sim.3923","article-title":"Generalized pairwise comparisons of prioritized outcomes in the two-sample problem","volume":"29","author":"Buyse","year":"2010","journal-title":"Statistics in Medicine"},{"key":"2024013111545919800_biom13920-bib-0010","doi-asserted-by":"crossref","first-page":"419","DOI":"10.2307\/2983440","article-title":"Model uncertainty, data mining and statistical inference","volume":"158","author":"Chatfield","year":"1995","journal-title":"Journal of the Royal Statistical Society. Series A"},{"key":"2024013111545919800_biom13920-bib-0011","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1038\/jid.2011.450","article-title":"Defining keratin protein function in skin epithelia: epidermolysis bullosa simplex and its aftermath","volume":"132","author":"Coulombe","year":"2012","journal-title":"Journal of Investigative Dermatology"},{"key":"2024013111545919800_biom13920-bib-0012","article-title":"Consort 2010 statement: extension to randomised crossover trials","volume":"366","author":"Dwan","year":"2019","journal-title":"BMJ"},{"key":"2024013111545919800_biom13920-bib-0013","volume-title":"Package \u2018Barnard'","author":"Erguler","year":"2016"},{"key":"2024013111545919800_biom13920-bib-0014","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1002\/(SICI)1097-0258(19990615)18:11<1341::AID-SIM129>3.0.CO;2-7","article-title":"Combining mortality and longitudinal measures in clinical trials","volume":"18","author":"Finkelstein","year":"1999","journal-title":"Statistics in Medicine"},{"key":"2024013111545919800_biom13920-bib-0015","article-title":"A neutral comparison of statistical methods for analyzing longitudinally measured ordinal outcomes in rare diseases","author":"Geroldinger","year":"2023","journal-title":"Biometrical Journal"},{"key":"2024013111545919800_biom13920-bib-0016","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1093\/biomet\/76.2.297","article-title":"Regression and time series model selection in small samples","volume":"76","author":"Hurvich","year":"1989","journal-title":"Biometrika"},{"key":"2024013111545919800_biom13920-bib-0017","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1214\/12-EJS714","article-title":"A studentized permutation test for the nonparametric Behrens\u2013Fisher problem in paired data","volume":"6","author":"Konietschke","year":"2012","journal-title":"Electronic Journal of Statistics"},{"key":"2024013111545919800_biom13920-bib-0018","doi-asserted-by":"crossref","first-page":"95","DOI":"10.2307\/2986114","article-title":"Logistic regression for correlated binary data","volume":"43","author":"le Cessie","year":"1994","journal-title":"Applied Statistics"},{"key":"2024013111545919800_biom13920-bib-0019","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1002\/sim.6344","article-title":"Small-sample performance of bias-corrected sandwich estimators for cluster-randomized trials with binary outcomes","volume":"34","author":"Li","year":"2015","journal-title":"Statistics in Medicine"},{"key":"2024013111545919800_biom13920-bib-0020","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1080\/00031305.2000.10474549","article-title":"Using heteroscedasticity consistent standard errors in the linear regression model","volume":"54","author":"Long","year":"2000","journal-title":"American Statistician"},{"key":"2024013111545919800_biom13920-bib-0021","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0304-4076(85)90158-7","article-title":"Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties","volume":"29","author":"MacKinnon","year":"1985","journal-title":"Journal of Econometrics"},{"key":"2024013111545919800_biom13920-bib-0022","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1214\/aoms\/1177730491","article-title":"On a test of whether one of two random variables is stochastically larger than the other","volume":"18","author":"Mann","year":"1947","journal-title":"The Annals of Mathematical Statistics"},{"key":"2024013111545919800_biom13920-bib-0023","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1177\/09622802221090761","article-title":"Robust statistical inference for matched win statistics","volume":"31","author":"Matsouaka","year":"2022","journal-title":"Statistical Methods in Medical Research"},{"key":"2024013111545919800_biom13920-bib-0024","first-page":"187","article-title":"Pseudo-likelihood estimation for incomplete data","volume":"21","author":"Molenberghs","year":"2011","journal-title":"Statistica Sinica"},{"key":"2024013111545919800_biom13920-bib-0025","volume-title":"Models for discrete longitudinal data","author":"Molenberghs","year":"2005"},{"key":"2024013111545919800_biom13920-bib-0026","first-page":"1","article-title":"nparld: an r software package for the nonparametric analysis of longitudinal data in factorial experiments","volume":"50","author":"Noguchi","year":"2012","journal-title":"Statistical Software"},{"key":"2024013111545919800_biom13920-bib-0027","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1093\/eurheartj\/ehr352","article-title":"The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities","volume":"33","author":"Pocock","year":"2012","journal-title":"European Heart Journal"},{"key":"2024013111545919800_biom13920-bib-0028","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1177\/09622802211046389","article-title":"Ranking procedures for repeated measures designs with missing data: estimation, testing and asymptotic theory","volume":"31","author":"Rubarth","year":"2022","journal-title":"Statistical Methods in Medical Research"},{"key":"2024013111545919800_biom13920-bib-0029","volume-title":"The FREQ procedures","author":"SAS Help Center","year":"2020"},{"key":"2024013111545919800_biom13920-bib-0030","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1177\/0962280220966629","article-title":"Unbiasedness and efficiency of non-parametric and umvue estimators of the probabilistic index and related statistics","volume":"30","author":"Verbeeck","year":"2021","journal-title":"Statistical Methods in Medical Research"},{"issue":"5","key":"2024013111545919800_biom13920-bib-0031","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1080\/10543406.2020.1730873","article-title":"Evaluation of inferential methods for the net benefit and win ratio statistics","volume":"30","author":"Verbeeck","year":"2020","journal-title":"Journal of Biopharmaceutical Statistics"},{"key":"2024013111545919800_biom13920-bib-0032","doi-asserted-by":"crossref","first-page":"5641","DOI":"10.1002\/sim.8388","article-title":"Generalized pairwise comparison methods to analyze (non)prioritized composite endpoints","volume":"38","author":"Verbeeck","year":"2019","journal-title":"Statistics in Medicine"},{"key":"2024013111545919800_biom13920-bib-0033","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1016\/j.jaad.2018.01.019","article-title":"Diacerein orphan drug development for epidermolysis bullosa simplex: a phase 2\/3 randomized, placebo-controlled, double-blind clinical trial","volume":"78","author":"Wally","year":"2018","journal-title":"Journal of the American Academy of Dermatology"},{"key":"2024013111545919800_biom13920-bib-0034","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1080\/01621459.1927.10502953","article-title":"Probable inference, the law of succession, and statistical inference","volume":"22","author":"Wilson","year":"1927","journal-title":"Journal of the American Statistical Association"}],"container-title":["Biometrics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/79\/4\/3998\/56396877\/biometrics_79_4_3998.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/79\/4\/3998\/56396877\/biometrics_79_4_3998.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T12:45:43Z","timestamp":1729946743000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biometrics\/article\/79\/4\/3998\/7587605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,16]]},"references-count":34,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,8,16]]},"published-print":{"date-parts":[[2023,12,1]]}},"URL":"https:\/\/doi.org\/10.1111\/biom.13920","relation":{},"ISSN":["0006-341X","1541-0420"],"issn-type":[{"value":"0006-341X","type":"print"},{"value":"1541-0420","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,12]]},"published":{"date-parts":[[2023,8,16]]},"assertion":[{"value":"2023-03-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-07-26","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-08-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}