Meta-analysis can be formulated as combining $p$-values across studies into a joint $p$-value function, from which point estimates and confidence intervals can be derived. We extend the meta-analytic estimation framework based on combined $p$-value functions to incorporate uncertainty in heterogeneity estimation by employing a confidence distribution approach. Specifically, the confidence distribution of Edgington's method is adjusted according to the confidence distribution of the heterogeneity parameter constructed from the generalized heterogeneity statistic. Simulation results suggest that 95% confidence intervals approach nominal coverage under most scenarios involving more than three studies and heterogeneity. Under no heterogeneity or for only three studies, the confidence interval typically overcovers, but is often narrower than the Hartung-Knapp-Sidik-Jonkman interval. The point estimator exhibits small bias under model misspecification and moderate to large heterogeneity. Edgington's method provides a practical alternative to classical approaches, with adjustment for heterogeneity estimation uncertainty often improving confidence interval coverage.

翻译：元分析可表述为将各研究中的$p$值合并为联合$p$值函数，并从中推导点估计与置信区间。本研究通过采用置信分布方法，将基于合并$p$值函数的元分析估计框架扩展至包含异质性估计的不确定性。具体而言，根据广义异质性统计量构建的异质性参数置信分布，对Edgington方法的置信分布进行校正。模拟结果表明，在涉及三个以上研究且存在异质性的大多数情境下，95%置信区间可接近名义覆盖水平。当不存在异质性或仅包含三个研究时，置信区间通常呈现过度覆盖现象，但其宽度往往小于Hartung-Knapp-Sidik-Jonkman区间。在模型设定错误及中高程度异质性条件下，点估计量表现出较小的偏差。Edgington方法为经典元分析提供了实用替代方案，其对异质性估计不确定性的校正通常能提升置信区间的覆盖性能。