Division of Biostatistics, German Cancer Research Center, Heidelberg, Germany.
Biometrics. 2020 Mar;76(1):326-336. doi: 10.1111/biom.13124. Epub 2019 Sep 13.
Bayesian methods allow borrowing of historical information through prior distributions. The concept of prior effective sample size (prior ESS) facilitates quantification and communication of such prior information by equating it to a sample size. Prior information can arise from historical observations; thus, the traditional approach identifies the ESS with such a historical sample size. However, this measure is independent of newly observed data, and thus would not capture an actual "loss of information" induced by the prior in case of prior-data conflict. We build on a recent work to relate prior impact to the number of (virtual) samples from the current data model and introduce the effective current sample size (ECSS) of a prior, tailored to the application in Bayesian clinical trial designs. Special emphasis is put on robust mixture, power, and commensurate priors. We apply the approach to an adaptive design in which the number of recruited patients is adjusted depending on the effective sample size at an interim analysis. We argue that the ECSS is the appropriate measure in this case, as the aim is to save current (as opposed to historical) patients from recruitment. Furthermore, the ECSS can help overcome lack of consensus in the ESS assessment of mixture priors and can, more broadly, provide further insights into the impact of priors. An R package accompanies the paper.
贝叶斯方法允许通过先验分布借用历史信息。先验有效样本量（prior ESS）的概念通过将其等同于样本量来促进对这种先验信息的量化和交流。先验信息可以来自历史观测；因此，传统方法将 ESS 与历史样本量相关联。然而，该度量与新观测到的数据独立，因此在存在先验数据冲突的情况下，不会捕获先验引起的实际“信息损失”。我们基于最近的一项工作，将先验的影响与当前数据模型中的（虚拟）样本数量相关联，并引入了先验的有效当前样本量（ECSS），适用于贝叶斯临床试验设计中的应用。特别强调稳健混合、功效和相称先验。我们将该方法应用于自适应设计中，其中根据中期分析的有效样本量调整招募的患者数量。我们认为在这种情况下，ECSS 是合适的度量，因为目的是从招募中拯救当前（而不是历史）患者。此外，ECSS 可以帮助克服混合先验 ESS 评估中的共识缺乏问题，并且更广泛地提供对先验影响的进一步见解。本文附有一个 R 包。
