The Letter Pi : Bayesian interpretation of p-values, Reproducibility and Considerations for Replication in the Generalized Linear Model
Pi值：广义线性模型中p值的贝叶斯解释与研究复现AI 解读 ↓
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Pi值：广义线性模型中p值的贝叶斯解释与研究复现
- 研究问题
- 广义线性模型中的p值能否通过后验尾部概率获得贝叶斯解释，并结合重复研究中的随机变化改进面向复现的统计分析。
- 方法与思路
- 作者提出对后验尾部概率即pi值设阈值的决策分析框架，讨论其与p值的对应，并以预测概率分析重复研究结果的波动。
- 材料陈述的贡献
- 摘要称，研究提出融合似然与贝叶斯分析的复现框架，以近期心代谢及肾脏疾病随机试验说明概念，并提供实现方法的R代码。
- 阅读关注点
- 应核对p值与pi值对应所需的先验和模型条件、决策阈值的损失设定，以及重复概率的定义和对不同研究设计的适用性。
- 阅读边界
- 这是arXiv预印本，同行评审或期刊接收未核实；摘要未说明概率对应的具体条件，不能据此把任意p值直接解释为后验概率。
原文摘要
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.