{"title":"On partial likelihood","authors":"N Reid","doi":"10.1093/jrsssa/qnae008","DOIUrl":null,"url":null,"abstract":"<jats:title>Abstract</jats:title> Partial likelihood, introduced in Cox (1975, Partial likelihood. Biometrika, 62(2),269–276), formalizes the construction of the inference function developed in Cox (1972, Regression models and life-tables (with discussion). Journal of the Royal Statistical Society Series B, 34(2),187–220) and referred there to as a conditional likelihood. Partial likelihood can also be viewed as a version of composite likelihood, a different example of which was studied in Cox, and Reid (2004, A note on pseudolikelihood constructed from marginal densities. Biometrika, 91(3),729–737). In this note, I describe the links between partial and composite likelihood, and the connections to profile, marginal, and conditional likelihood. Somewhat tangentially, two recent applications of the Cox proportional hazards model from the medical literature are briefly discussed, as they highlight the model’s ongoing relevance while also raising some more general questions about inference.","PeriodicalId":517419,"journal":{"name":"The Journal of the Royal Statistical Society, Series A (Statistics in Society)","volume":"203 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of the Royal Statistical Society, Series A (Statistics in Society)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/jrsssa/qnae008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract Partial likelihood, introduced in Cox (1975, Partial likelihood. Biometrika, 62(2),269–276), formalizes the construction of the inference function developed in Cox (1972, Regression models and life-tables (with discussion). Journal of the Royal Statistical Society Series B, 34(2),187–220) and referred there to as a conditional likelihood. Partial likelihood can also be viewed as a version of composite likelihood, a different example of which was studied in Cox, and Reid (2004, A note on pseudolikelihood constructed from marginal densities. Biometrika, 91(3),729–737). In this note, I describe the links between partial and composite likelihood, and the connections to profile, marginal, and conditional likelihood. Somewhat tangentially, two recent applications of the Cox proportional hazards model from the medical literature are briefly discussed, as they highlight the model’s ongoing relevance while also raising some more general questions about inference.
摘要 部分似然法由 Cox（1975，Partial likelihood.Biometrika，62(2),269-276）中提出的部分似然法，将考克斯（1972，回归模型和生命表（附讨论）。英国皇家统计学会期刊 B 辑，34（2），187-220）中提出的推理函数的构造形式化，并将其称为条件似然。部分似然也可视为复合似然的一个版本，Cox 和 Reid（2004，A note on pseudolikelihood constructed from marginal densities.Biometrika，91（3），729-737）。在本说明中，我将介绍部分似然与复合似然之间的联系，以及与轮廓似然、边际似然和条件似然之间的联系。本文从切入点出发，简要讨论了医学文献中对考克斯比例危险模型的两个最新应用，因为它们突出了该模型的持续相关性，同时也提出了一些关于推理的一般性问题。
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