Meta-analytic methods tend to take all-or-nothing approaches to study-level heterogeneity, assuming all studies are heterogeneous or homogeneous, leading to inefficiency and/or bias in estimation and inference. In this paper, we develop a heterogeneity-adaptive meta-analysis in linear models that adapts to the amount of information shared between datasets. The primary mechanism for the information-sharing is a shrinkage of dataset-specific distributions towards a new "centroid" distribution through a Kullback-Leibler divergence penalty. The Kullback-Leibler divergence is uniquely geometrically suited for measuring relative information between datasets, and leads to relatively simple closed form estimators with intuitive interpretations. We establish our estimator's desirable inferential properties without assuming homogeneity of dataset parameters. Among other results, we show that our estimator has a provably smaller mean squared error than the dataset-specific maximum likelihood estimators, and establish asymptotically valid inference procedures. A comprehensive set of simulations highlights our estimator's versatility, and an analysis of data from the eICU Collaborative Research Database illustrates its performance in a real-world setting.

翻译：元分析方法在处理研究间异质性时往往采取全有或全无的策略，即假设所有研究均存在异质性或同质性，这导致估计与推断的效率低下和/或偏差。本文在线性模型中提出了一种异质性自适应元分析方法，能够根据数据集间共享的信息量进行自适应调整。信息共享的核心机制是通过Kullback-Leibler散度惩罚，将数据集特定的分布向一个新的“质心”分布收缩。Kullback-Leibler散度在几何上特别适合衡量数据集间的相对信息，并导出了形式相对简单、具有直观解释的闭式估计量。我们在不假设数据集参数同质性的前提下，建立了该估计量理想的推断性质。除其他结果外，我们证明该估计量具有可证明小于数据集特定最大似然估计量的均方误差，并建立了渐近有效的推断程序。一系列综合模拟实验突显了该估计量的通用性，而对eICU协作研究数据库数据的分析则展示了其在真实场景中的性能。