Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that it is the improper use and errors in interpretation, rather than the p-values themselves that are to blame. Similar exchanges about the role of p-values have occurred with some regularity every 10 to 15 years since their formal introduction in statistical practice. The apparent contradiction between the repeated failures in interpretation and continuous use of p-values suggest that there is an inferential value in the computation of these values. In this work we propose to attach a radical Bayesian interpretation to the number computed and reported as a p-value for the Generalized Linear Model, which has been the workhorse of applied statistical work. We introduce a decision analytic framework for thresholding posterior tail areas (pi-values) which for any given Bayesian analysis will have a direct correspondence to p-values in non-Bayesian approaches. Pi-values are non-controversial, posterior probability summaries of treatment effects. A predictive probability argument is made to justify the exploration of the stochastic variation (replication probability) of p and pi-values and culminates into a concrete proposal for the synthesis of Likelihood and Bayesian approaches to data analyses that aim for reproducibility. We illustrate these concepts using the results of recent randomized controlled trials in cardiometabolic and kidney diseases and provide R code for the implementation of the proposed methodology.

翻译：基于p值的显著性检验已被指认为科学研究中可重复性危机的诱因之一，其中一项改革建议是废除p值转而采用贝叶斯分析。p值的捍卫者反驳称，问题根源在于不当使用与解释错误，而非p值本身。自p值正式引入统计实践以来，关于其作用的类似争论每隔10至15年便会周期性重现。解释屡次失误与p值持续使用之间的矛盾表明，该类数值的计算具有推断价值。本研究针对应用统计工作的主力工具——广义线性模型（Generalized Linear Model）中计算并报告的p值，提出赋予其彻底的贝叶斯解释。我们引入一个基于决策分析的阈值框架用于后验尾部概率（pi值），该框架下任意贝叶斯分析都能与非贝叶斯方法中的p值直接对应。Pi值是对处理效应的后验概率概括，且无争议性。通过预测概率论证，我们验证了探究p值与pi值随机变异（复制概率）的合理性，最终形成融合似然与贝叶斯方法以实现可重复性数据分析的具体方案。我们采用近期心代谢疾病与肾脏疾病随机对照试验的结果阐释上述概念，并提供实施所提方法的R代码。