基于广义线性混合模型的随机效应Meta分析：适用于少量研究的Bartlett校正方法
Random-effects meta-analysis via generalized linear mixed models: A Bartlett-corrected approach for few studies
AI总结：
针对少量研究下广义线性混合模型随机效应Meta分析的研究间方差低估问题，提出带简化Bartlett校正的轮廓似然法，兼具理论保障与良好的模拟和实证表现。
摘要：
随机效应模型是Meta分析的核心工具，但当纳入研究数量较少时，研究间方差常被低估。在这类场景下，置信区间会过窄，无法达到标称覆盖概率。尽管包括Bartlett校正在内的多种小样本校正方法已在正态-正态模型下被开发，但针对广义线性混合模型（GLMMs）的对应方法仍十分有限。本研究在GLMM框架内提出了一个统一的随机效应Meta分析框架，该框架仅依赖汇总数据，可适配指数族中任意分布的结局变量，包括二项分布、泊松分布和伽马分布。为改善少量研究下的区间估计效果，我们开发了带简化Bartlett校正的轮廓似然法（PLSBC），该方法无需计算高阶导数即可优化轮廓似然比统计量的卡方近似。我们从理论上证明，所提出的估计量保留了最大似然估计量的一致性和渐近正态性。模拟研究表明，PLSBC在多种结局类型下均能产生近乎无偏的估计，并维持标称覆盖率。对三项已发表的、分别涉及二项、泊松和伽马结局的Meta分析的应用显示，该方法在少量研究场景下能提供稳健且可解释的推断。因此，PLSBC为研究数量有限时的随机效应Meta分析提供了一个实用且适用广泛的框架。
英文摘要：
Random-effects models are central to meta-analysis, yet the between-study variance is often underestimated when the number of studies is small. In such settings, confidence intervals become unduly narrow and fail to attain the nominal coverage probability. Although several small-sample corrections, including the Bartlett correction, have been developed under the normal-normal model, corresponding methodology for generalized linear mixed models (GLMMs) remains limited. This study proposes a unified framework for random-effects meta-analysis within the GLMM that relies exclusively on aggregate data and accommodates outcomes that follow any distribution in the exponential family, including the binomial, Poisson, and gamma distributions. To improve interval estimation with few studies, we develop a profile likelihood method with a simplified Bartlett correction (PLSBC), which refines the chi-squared approximation of the profile likelihood ratio statistic without requiring higher-order derivatives. We show theoretically that the proposed estimators preserve the consistency and asymptotic normality of the maximum likelihood estimators. Simulation studies demonstrate that the PLSBC yields nearly unbiased estimates and maintains nominal coverage across a variety of outcome types. Applications to three published meta-analyses with binomial, Poisson, and gamma outcomes indicate that the proposed approach provides robust and interpretable inference with few studies. The PLSBC therefore offers a practical and broadly applicable framework for random-effects meta-analysis when the number of studies is limited.
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