{"title":"作为调和平均值的平均危险。","authors":"Yasutaka Chiba","doi":"10.1002/pst.70009","DOIUrl":null,"url":null,"abstract":"<p><p>A new measure was recently developed in the context of survival analysis that can be interpreted as a weighted arithmetic mean of the hazards with the survival function as the weight. However, when the average hazard is desired, it is more appropriate to use the harmonic mean rather than the arithmetic mean. Therefore, in this article, we derive the average hazard as a harmonic mean version of the expectation for hazards and show it to be equal to the previous weighted arithmetic mean. Furthermore, we demonstrate that the average hazard should be estimated using only the times at which the event is observed, while previous studies have allowed estimating the average hazard even when the truncation time is set to a time at which the event is not observed.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":"24 2","pages":"e70009"},"PeriodicalIF":1.3000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11893520/pdf/","citationCount":"0","resultStr":"{\"title\":\"Average Hazard as Harmonic Mean.\",\"authors\":\"Yasutaka Chiba\",\"doi\":\"10.1002/pst.70009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>A new measure was recently developed in the context of survival analysis that can be interpreted as a weighted arithmetic mean of the hazards with the survival function as the weight. However, when the average hazard is desired, it is more appropriate to use the harmonic mean rather than the arithmetic mean. Therefore, in this article, we derive the average hazard as a harmonic mean version of the expectation for hazards and show it to be equal to the previous weighted arithmetic mean. Furthermore, we demonstrate that the average hazard should be estimated using only the times at which the event is observed, while previous studies have allowed estimating the average hazard even when the truncation time is set to a time at which the event is not observed.</p>\",\"PeriodicalId\":19934,\"journal\":{\"name\":\"Pharmaceutical Statistics\",\"volume\":\"24 2\",\"pages\":\"e70009\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11893520/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pharmaceutical Statistics\",\"FirstCategoryId\":\"3\",\"ListUrlMain\":\"https://doi.org/10.1002/pst.70009\",\"RegionNum\":4,\"RegionCategory\":\"医学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"PHARMACOLOGY & PHARMACY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pharmaceutical Statistics","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1002/pst.70009","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHARMACOLOGY & PHARMACY","Score":null,"Total":0}
A new measure was recently developed in the context of survival analysis that can be interpreted as a weighted arithmetic mean of the hazards with the survival function as the weight. However, when the average hazard is desired, it is more appropriate to use the harmonic mean rather than the arithmetic mean. Therefore, in this article, we derive the average hazard as a harmonic mean version of the expectation for hazards and show it to be equal to the previous weighted arithmetic mean. Furthermore, we demonstrate that the average hazard should be estimated using only the times at which the event is observed, while previous studies have allowed estimating the average hazard even when the truncation time is set to a time at which the event is not observed.
期刊介绍：
Pharmaceutical Statistics is an industry-led initiative, tackling real problems in statistical applications. The Journal publishes papers that share experiences in the practical application of statistics within the pharmaceutical industry. It covers all aspects of pharmaceutical statistical applications from discovery, through pre-clinical development, clinical development, post-marketing surveillance, consumer health, production, epidemiology, and health economics.
The Journal is both international and multidisciplinary. It includes high quality practical papers, case studies and review papers.
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