🤖 AI Summary
Traditional meta-analysis methods often assume either complete homogeneity or complete heterogeneity across studies, which can lead to biased estimates or loss of efficiency. This work proposes a heterogeneity-adaptive meta-analysis framework that, within a linear model setting, shrinks individual study distributions toward a shared “centroid” via Kullback–Leibler (KL) divergence regularization, enabling geometrically natural and dynamic information sharing. By avoiding extreme assumptions about between-study variability, the method yields a closed-form estimator whose mean squared error is theoretically guaranteed to be strictly lower than that of the conventional maximum likelihood estimator. Simulation studies demonstrate the approach’s flexibility and robustness, while an application to real-world data from the eICU Collaborative Research Database further confirms its practical effectiveness.
📝 Abstract
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.