Silvia Calderazzo, Manuel Wiesenfarth, Annette Kopp-Schneider
{"title":"Robust incorporation of historical information with known type I error rate inflation","authors":"Silvia Calderazzo, Manuel Wiesenfarth, Annette Kopp-Schneider","doi":"10.1002/bimj.202200322","DOIUrl":null,"url":null,"abstract":"<p>Bayesian clinical trials can benefit from available historical information through the specification of informative prior distributions. Concerns are however often raised about the potential for prior-data conflict and the impact of Bayes test decisions on frequentist operating characteristics, with particular attention being assigned to inflation of type I error (TIE) rates. This motivates the development of principled borrowing mechanisms, that strike a balance between frequentist and Bayesian decisions. Ideally, the trust assigned to historical information defines the degree of robustness to prior-data conflict one is willing to sacrifice. However, such relationship is often not directly available when explicitly considering inflation of TIE rates. We build on available literature relating frequentist and Bayesian test decisions, and investigate a rationale for inflation of TIE rate which explicitly and linearly relates the amount of borrowing and the amount of TIE rate inflation in one-arm studies. A novel dynamic borrowing mechanism tailored to hypothesis testing is additionally proposed. We show that, while dynamic borrowing prevents the possibility to obtain a simple closed-form TIE rate computation, an explicit upper bound can still be enforced. Connections with the robust mixture prior approach, particularly in relation to the choice of the mixture weight and robust component, are made. Simulations are performed to show the properties of the approach for normal and binomial outcomes, and an exemplary application is demonstrated in a case study.</p>","PeriodicalId":55360,"journal":{"name":"Biometrical Journal","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/bimj.202200322","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biometrical Journal","FirstCategoryId":"99","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/bimj.202200322","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
Bayesian clinical trials can benefit from available historical information through the specification of informative prior distributions. Concerns are however often raised about the potential for prior-data conflict and the impact of Bayes test decisions on frequentist operating characteristics, with particular attention being assigned to inflation of type I error (TIE) rates. This motivates the development of principled borrowing mechanisms, that strike a balance between frequentist and Bayesian decisions. Ideally, the trust assigned to historical information defines the degree of robustness to prior-data conflict one is willing to sacrifice. However, such relationship is often not directly available when explicitly considering inflation of TIE rates. We build on available literature relating frequentist and Bayesian test decisions, and investigate a rationale for inflation of TIE rate which explicitly and linearly relates the amount of borrowing and the amount of TIE rate inflation in one-arm studies. A novel dynamic borrowing mechanism tailored to hypothesis testing is additionally proposed. We show that, while dynamic borrowing prevents the possibility to obtain a simple closed-form TIE rate computation, an explicit upper bound can still be enforced. Connections with the robust mixture prior approach, particularly in relation to the choice of the mixture weight and robust component, are made. Simulations are performed to show the properties of the approach for normal and binomial outcomes, and an exemplary application is demonstrated in a case study.
贝叶斯临床试验可以通过指定信息丰富的先验分布,从可用的历史信息中获益。然而,人们经常担心先验数据冲突的可能性以及贝叶斯检验决策对频繁主义操作特征的影响,尤其关注 I 型误差(TIE)率的膨胀。这就促使人们开发有原则的借用机制,在频繁主义和贝叶斯决策之间取得平衡。理想情况下,对历史信息的信任程度决定了人们愿意牺牲先验数据冲突的稳健程度。然而,在明确考虑 TIE 率膨胀时,这种关系往往无法直接获得。我们以现有的有关频数主义和贝叶斯检验决策的文献为基础,研究了单臂研究中借用量与 TIE 率膨胀量之间明确的线性关系的 TIE 率膨胀原理。此外,我们还提出了一种为假设检验量身定制的新型动态借用机制。我们证明,虽然动态借用无法获得简单的闭式 TIE 率计算,但仍可执行明确的上限。我们还提出了与稳健混合先验方法的联系,特别是在混合权重和稳健成分的选择方面。我们还进行了模拟,以显示该方法在正态和二项式结果中的特性,并在案例研究中演示了一个示例应用。
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.