Division of Biostatistics, German Cancer Research Center, Im Neuenheimer Feld 581, 69120 Heidelberg, Germany.
Biostatistics. 2022 Jan 13;23(1):328-344. doi: 10.1093/biostatistics/kxaa027.
Bayesian clinical trials allow taking advantage of relevant external information through the elicitation of prior distributions, which influence Bayesian posterior parameter estimates and test decisions. However, incorporation of historical information can have harmful consequences on the trial's frequentist (conditional) operating characteristics in case of inconsistency between prior information and the newly collected data. A compromise between meaningful incorporation of historical information and strict control of frequentist error rates is therefore often sought. Our aim is thus to review and investigate the rationale and consequences of different approaches to relaxing strict frequentist control of error rates from a Bayesian decision-theoretic viewpoint. In particular, we define an integrated risk which incorporates losses arising from testing, estimation, and sampling. A weighted combination of the integrated risk addends arising from testing and estimation allows moving smoothly between these two targets. Furthermore, we explore different possible elicitations of the test error costs, leading to test decisions based either on posterior probabilities, or solely on Bayes factors. Sensitivity analyses are performed following the convention which makes a distinction between the prior of the data-generating process, and the analysis prior adopted to fit the data. Simulation in the case of normal and binomial outcomes and an application to a one-arm proof-of-concept trial, exemplify how such analysis can be conducted to explore sensitivity of the integrated risk, the operating characteristics, and the optimal sample size, to prior-data conflict. Robust analysis prior specifications, which gradually discount potentially conflicting prior information, are also included for comparison. Guidance with respect to cost elicitation, particularly in the context of a Phase II proof-of-concept trial, is provided.
贝叶斯临床试验允许通过启发先验分布来利用相关的外部信息，这些信息会影响贝叶斯后验参数估计和检验决策。然而，如果先验信息与新收集的数据不一致，那么纳入历史信息可能会对试验的频率主义（条件）操作特征产生有害影响。因此，通常会在有意义地纳入历史信息和严格控制频率主义错误率之间寻求妥协。我们的目的是从贝叶斯决策理论的角度回顾和研究放宽对错误率的严格频率主义控制的不同方法的原理和后果。特别是，我们定义了一个综合风险，该风险包含了来自检验、估计和抽样的损失。测试和估计的综合风险加项的加权组合允许在这两个目标之间平稳移动。此外，我们还探索了不同的可能的检验误差成本的启发式方法，导致基于后验概率或仅基于贝叶斯因子的检验决策。敏感性分析遵循了区分数据生成过程的先验和用于拟合数据的分析先验的传统。正态和二项分布结果的模拟以及对单臂概念验证试验的应用，说明了如何进行这种分析，以探索综合风险、操作特征和最优样本量对先验-数据冲突的敏感性。还包括了逐步折扣潜在冲突的先验信息的稳健分析先验规范，以供比较。提供了有关成本启发的指导，特别是在 II 期概念验证试验的背景下。
