{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:34:10Z","timestamp":1760060050510,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T00:00:00Z","timestamp":1753574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007957","name":"Chongqing Municipal Education Commission","doi-asserted-by":"publisher","award":["KJZD-K202201101","CSTB2024NSCQ-LZX0136"],"award-info":[{"award-number":["KJZD-K202201101","CSTB2024NSCQ-LZX0136"]}],"id":[{"id":"10.13039\/501100007957","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Chongqing, China","award":["KJZD-K202201101","CSTB2024NSCQ-LZX0136"],"award-info":[{"award-number":["KJZD-K202201101","CSTB2024NSCQ-LZX0136"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Crossover trials are specifically designed to evaluate treatment effects within individual participants through within-subject comparisons. In a standard AB\/BA crossover trial, participants are randomly allocated to one of two treatment sequences: either the AB sequence (where patients receive treatment A first and then cross over to treatment B after a washout period) or the BA sequence (where patients receive B first and then cross over to A after a washout period). Asymptotic and approximate unconditional test procedures, based on two Wald-type statistics, the likelihood ratio statistic, and the score test statistic for the odds ratio (OR), are developed to evaluate the equality of treatment effects in this trial design. Additionally, confidence intervals for OR are constructed, accompanied by an approximate sample size calculation methodology to control the interval width at a pre-specified precision. Empirical analyses demonstrate that asymptotic test procedures exhibit robust performance in moderate to large sample sizes, though they occasionally yield unsatisfactory type I error rates when the sample size is small. In such cases, approximate unconditional test procedures emerge as a rigorous alternative. All proposed confidence intervals achieve satisfactory coverage probabilities, and the approximate sample size estimation method demonstrates high accuracy, as evidenced by empirical coverage probabilities aligning closely with pre-specified confidence levels under estimated sample sizes. To validate practical utility, two real examples are used to illustrate the proposed methodologies.<\/jats:p>","DOI":"10.3390\/axioms14080582","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T09:53:02Z","timestamp":1753696382000},"page":"582","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Equivalence Test and Sample Size Determination Based on Odds Ratio in an AB\/BA Crossover Study with Binary Outcomes"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3262-9535","authenticated-orcid":false,"given":"Shi-Fang","family":"Qiu","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue-Qin","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wai-Yin","family":"Poon","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"ref_1","first-page":"7","article-title":"The two-period cross-over clinical trial","volume":"8","author":"Hills","year":"1979","journal-title":"Br. 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