{"title":"重叠指数的推理:与癌症数据的应用。","authors":"Raju Dey, Arne C Bathke, Somesh Kumar","doi":"10.1515/ijb-2024-0106","DOIUrl":null,"url":null,"abstract":"<p><p>The quantification of overlap between two distributions has applications in various fields of biology, medical, genetic, and ecological research. In this article, new overlap and containment indices are considered for quantifying the niche overlap between two species/populations. Some new properties of these indices are established and the problem of estimation is studied, when the two distributions are exponential with different scale parameters. We propose several estimators and compare their relative performance with respect to different loss functions. The asymptotic normality of the maximum likelihood estimators of these indices is proved under certain conditions. We also obtain confidence intervals of the indices based on three different approaches and compare their average lengths and coverage probabilities. The point and confidence interval procedures developed here are applied on a breast cancer data set to analyze the similarity between the survival times of patients undergoing two different types of surgery. Additionally, the similarity between the relapse free times of these two sets of patients is also studied.</p>","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inference on overlap index: with an application to cancer data.\",\"authors\":\"Raju Dey, Arne C Bathke, Somesh Kumar\",\"doi\":\"10.1515/ijb-2024-0106\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The quantification of overlap between two distributions has applications in various fields of biology, medical, genetic, and ecological research. In this article, new overlap and containment indices are considered for quantifying the niche overlap between two species/populations. Some new properties of these indices are established and the problem of estimation is studied, when the two distributions are exponential with different scale parameters. We propose several estimators and compare their relative performance with respect to different loss functions. The asymptotic normality of the maximum likelihood estimators of these indices is proved under certain conditions. We also obtain confidence intervals of the indices based on three different approaches and compare their average lengths and coverage probabilities. The point and confidence interval procedures developed here are applied on a breast cancer data set to analyze the similarity between the survival times of patients undergoing two different types of surgery. Additionally, the similarity between the relapse free times of these two sets of patients is also studied.</p>\",\"PeriodicalId\":50333,\"journal\":{\"name\":\"International Journal of Biostatistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-09-05\",\"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-2024-0106\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Biostatistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ijb-2024-0106","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Inference on overlap index: with an application to cancer data.
The quantification of overlap between two distributions has applications in various fields of biology, medical, genetic, and ecological research. In this article, new overlap and containment indices are considered for quantifying the niche overlap between two species/populations. Some new properties of these indices are established and the problem of estimation is studied, when the two distributions are exponential with different scale parameters. We propose several estimators and compare their relative performance with respect to different loss functions. The asymptotic normality of the maximum likelihood estimators of these indices is proved under certain conditions. We also obtain confidence intervals of the indices based on three different approaches and compare their average lengths and coverage probabilities. The point and confidence interval procedures developed here are applied on a breast cancer data set to analyze the similarity between the survival times of patients undergoing two different types of surgery. Additionally, the similarity between the relapse free times of these two sets of patients is also studied.
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.