{"title":"Online false discovery rate control for LORD++ and SAFFRON under positive, local dependence","authors":"Aaron Fisher","doi":"10.1002/bimj.202300177","DOIUrl":null,"url":null,"abstract":"<p>Online testing procedures assume that hypotheses are observed in sequence, and allow the significance thresholds for upcoming tests to depend on the test statistics observed so far. Some of the most popular online methods include alpha investing, LORD++, and SAFFRON. These three methods have been shown to provide online control of the “modified” false discovery rate (mFDR) under a condition known as CS. However, to our knowledge, LORD++ and SAFFRON have only been shown to control the traditional false discovery rate (FDR) under an independence condition on the test statistics. Our work bolsters these results by showing that SAFFRON and LORD++ additionally ensure online control of the FDR under a “local” form of nonnegative dependence. Further, FDR control is maintained under certain types of adaptive stopping rules, such as stopping after a certain number of rejections have been observed. Because alpha investing can be recovered as a special case of the SAFFRON framework, our results immediately apply to alpha investing as well. In the process of deriving these results, we also formally characterize how the conditional super-uniformity assumption implicitly limits the allowed <i>p</i>-value dependencies. This implicit limitation is important not only to our proposed FDR result, but also to many existing mFDR results.</p>","PeriodicalId":55360,"journal":{"name":"Biometrical Journal","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biometrical Journal","FirstCategoryId":"99","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/bimj.202300177","RegionNum":3,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
Online testing procedures assume that hypotheses are observed in sequence, and allow the significance thresholds for upcoming tests to depend on the test statistics observed so far. Some of the most popular online methods include alpha investing, LORD++, and SAFFRON. These three methods have been shown to provide online control of the “modified” false discovery rate (mFDR) under a condition known as CS. However, to our knowledge, LORD++ and SAFFRON have only been shown to control the traditional false discovery rate (FDR) under an independence condition on the test statistics. Our work bolsters these results by showing that SAFFRON and LORD++ additionally ensure online control of the FDR under a “local” form of nonnegative dependence. Further, FDR control is maintained under certain types of adaptive stopping rules, such as stopping after a certain number of rejections have been observed. Because alpha investing can be recovered as a special case of the SAFFRON framework, our results immediately apply to alpha investing as well. In the process of deriving these results, we also formally characterize how the conditional super-uniformity assumption implicitly limits the allowed p-value dependencies. This implicit limitation is important not only to our proposed FDR result, but also to many existing mFDR results.
期刊介绍:
Biometrical Journal publishes papers on statistical methods and their applications in life sciences including medicine, environmental sciences and agriculture. Methodological developments should be motivated by an interesting and relevant problem from these areas. Ideally the manuscript should include a description of the problem and a section detailing the application of the new methodology to the problem. Case studies, review articles and letters to the editors are also welcome. Papers containing only extensive mathematical theory are not suitable for publication in Biometrical Journal.