AI 中文总结
针对罕见事件比例元分析中常用最大似然估计器存在有限样本偏差的问题，提出最大惩罚似然估计器，通过最大化Jeffreys先验惩罚增强的对数似然得到，模拟显示其在多方面优于普通MLE，还引入新置信区间，为相关元分析提供有用替代方法。
AI 中文摘要
在比例的元分析中，感兴趣的事件通常很罕见，导致事件计数稀疏且常有零事件研究。β-二项式模型已被用作灵活的随机效应模型来汇总过度分散和罕见事件比例。然而，常用的最大似然估计器（MLE）可能存在有限样本偏差，在研究数量少或平均事件概率接近边界时尤为明显。本文提出了一种用于β-二项式随机效应模型的最大惩罚似然估计器。该估计器通过最大化由Jeffreys先验惩罚增强的对数似然得到，在一系列稀疏数据模型中显示出良好的有限样本偏差和稳定性。除了Wald型置信区间（CIs），还引入了轮廓惩罚似然CIs作为稀疏数据设置中更可靠的推断方法。模拟研究表明，该估计器在收敛速度、偏差和均方根误差方面通常优于普通MLE，特别是在研究较少或事件概率较低的情况下。此外，轮廓惩罚似然CIs有效地保持了覆盖率接近名义水平。该方法为罕见事件比例的元分析提供了一种有用的替代普通MLE的方法。
英文摘要
Meta-analyses of proportions often involve sparse event counts and zero-event studies. The beta-binomial model has been used as a flexible random-effects model for pooling overdispersed and rare-event proportions. However, the ordinary maximum likelihood estimator (MLE) may suffer from finite-sample bias when few studies are available or the mean event probability is close to the boundary. In this article, we propose a maximum penalized likelihood estimator based on the Jeffreys-prior penalty, which has shown favorable finite-sample bias and stability properties in sparse-data models. We also develop Wald-type and profile penalized likelihood confidence intervals (CIs). In a simulation study, the proposed estimator generally achieved higher convergence rates, lower bias, and lower root mean squared error than the ordinary MLE, particularly with fewer studies or lower event probabilities. Additionally, the profile penalized likelihood CIs maintained coverage close to the nominal level. The proposed method provides a useful alternative for meta-analyses of rare-event proportions.
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