{"title":"An improved estimator of the logarithmic odds ratio for small sample sizes using a Bayesian approach.","authors":"Toru Ogura, Takemi Yanagimoto","doi":"10.1515/ijb-2024-0105","DOIUrl":null,"url":null,"abstract":"<p><p>The logarithmic odds ratio is a well-known method for comparing binary data between two independent groups. Although various existing methods proposed for estimating a logarithmic odds ratio, most methods estimate two proportions in each group independently and then estimate the logarithmic odds ratio using the two estimated proportions. When using a logarithmic odds ratio, researchers are more interested in the logarithmic odds ratio than proportions for each group. Parameter estimations, generally, incur random and systematic errors. These errors in initially estimated parameter may affect later estimated parameter. We propose a Bayesian estimator to directly estimate a logarithmic odds ratio without using proportions for each group. Many existing methods need to estimate two parameters (two proportions in each group) to estimate a logarithmic odds ratio; however, the proposed method only estimates one parameter (logarithmic odds ratio). Therefore, the proposed estimator can be closer to the population's logarithmic odds ratio than existing estimators. Additionally, the validity of the proposed estimator is verified using numerical calculations and applications.</p>","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Biostatistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ijb-2024-0105","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The logarithmic odds ratio is a well-known method for comparing binary data between two independent groups. Although various existing methods proposed for estimating a logarithmic odds ratio, most methods estimate two proportions in each group independently and then estimate the logarithmic odds ratio using the two estimated proportions. When using a logarithmic odds ratio, researchers are more interested in the logarithmic odds ratio than proportions for each group. Parameter estimations, generally, incur random and systematic errors. These errors in initially estimated parameter may affect later estimated parameter. We propose a Bayesian estimator to directly estimate a logarithmic odds ratio without using proportions for each group. Many existing methods need to estimate two parameters (two proportions in each group) to estimate a logarithmic odds ratio; however, the proposed method only estimates one parameter (logarithmic odds ratio). Therefore, the proposed estimator can be closer to the population's logarithmic odds ratio than existing estimators. Additionally, the validity of the proposed estimator is verified using numerical calculations and applications.
期刊介绍:
The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.