José L Jiménez, Isobel Barrott, Francesca Gasperoni, Dominic Magirr
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Test statistics based on the RMST, on the other hand, allow one to investigate the average difference between two survival curves up to a pre-specified time point <math> <semantics><mrow><mi>τ</mi></mrow> <annotation>$$ \\tau $$</annotation></semantics> </math> -a mathematically unambiguous summary measure. However, by emphasizing differences prior to <math> <semantics><mrow><mi>τ</mi></mrow> <annotation>$$ \\tau $$</annotation></semantics> </math> , such test statistics may not fully capture the benefit of a new treatment in terms of long-term survival. In this article, we introduce a graphical approach for direct comparison of weighted log-rank tests and tests based on the RMST. This new perspective allows a more informed choice of the analysis method, going beyond power and type I error comparison.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Visualizing hypothesis tests in survival analysis under anticipated delayed effects.\",\"authors\":\"José L Jiménez, Isobel Barrott, Francesca Gasperoni, Dominic Magirr\",\"doi\":\"10.1002/pst.2393\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>What can be considered an appropriate statistical method for the primary analysis of a randomized clinical trial (RCT) with a time-to-event endpoint when we anticipate non-proportional hazards owing to a delayed effect? This question has been the subject of much recent debate. The standard approach is a log-rank test and/or a Cox proportional hazards model. Alternative methods have been explored in the statistical literature, such as weighted log-rank tests and tests based on the Restricted Mean Survival Time (RMST). While weighted log-rank tests can achieve high power compared to the standard log-rank test, some choices of weights may lead to type-I error inflation under particular conditions. In addition, they are not linked to a mathematically unambiguous summary measure. Test statistics based on the RMST, on the other hand, allow one to investigate the average difference between two survival curves up to a pre-specified time point <math> <semantics><mrow><mi>τ</mi></mrow> <annotation>$$ \\\\tau $$</annotation></semantics> </math> -a mathematically unambiguous summary measure. However, by emphasizing differences prior to <math> <semantics><mrow><mi>τ</mi></mrow> <annotation>$$ \\\\tau $$</annotation></semantics> </math> , such test statistics may not fully capture the benefit of a new treatment in terms of long-term survival. In this article, we introduce a graphical approach for direct comparison of weighted log-rank tests and tests based on the RMST. This new perspective allows a more informed choice of the analysis method, going beyond power and type I error comparison.</p>\",\"PeriodicalId\":19934,\"journal\":{\"name\":\"Pharmaceutical Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pharmaceutical Statistics\",\"FirstCategoryId\":\"3\",\"ListUrlMain\":\"https://doi.org/10.1002/pst.2393\",\"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.2393","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHARMACOLOGY & PHARMACY","Score":null,"Total":0}
Visualizing hypothesis tests in survival analysis under anticipated delayed effects.
What can be considered an appropriate statistical method for the primary analysis of a randomized clinical trial (RCT) with a time-to-event endpoint when we anticipate non-proportional hazards owing to a delayed effect? This question has been the subject of much recent debate. The standard approach is a log-rank test and/or a Cox proportional hazards model. Alternative methods have been explored in the statistical literature, such as weighted log-rank tests and tests based on the Restricted Mean Survival Time (RMST). While weighted log-rank tests can achieve high power compared to the standard log-rank test, some choices of weights may lead to type-I error inflation under particular conditions. In addition, they are not linked to a mathematically unambiguous summary measure. Test statistics based on the RMST, on the other hand, allow one to investigate the average difference between two survival curves up to a pre-specified time point -a mathematically unambiguous summary measure. However, by emphasizing differences prior to , such test statistics may not fully capture the benefit of a new treatment in terms of long-term survival. In this article, we introduce a graphical approach for direct comparison of weighted log-rank tests and tests based on the RMST. This new perspective allows a more informed choice of the analysis method, going beyond power and type I error comparison.
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.