Meta-analysis allows rigorous aggregation of estimates and uncertainty across multiple studies. When a given study reports multiple estimates, such as log odds ratios (ORs) or log relative risks (RRs) across exposure groups, accounting for within-study correlations improves accuracy and efficiency of meta-analytic results. Canonical approaches of Greenland-Longnecker and Hamling estimate pseudo cases and non-cases for exposure groups to obtain within-study correlations. However, currently available implementations for both methods fail on simple examples. We review both GL and Hamling methods through the lens of optimization. For ORs, we provide modifications of each approach that ensure convergence for any feasible inputs. For GL, this is achieved through a new connection to entropic minimization. For Hamling, a modification leads to a provably solvable equivalent set of equations given a specific initialization. For each, we provide implementations a guaranteed to work for any feasible input. For RRs, we show the new GL approach is always guaranteed to succeed, but any Hamling approach may fail: we give counter-examples where no solutions exist. We derive a sufficient condition on reported RRs that guarantees success when reported variances are all equal.

翻译：荟萃分析能够严谨地整合多项研究的估计值及其不确定性。当某项研究报告了多个估计值（例如不同暴露组的对数比值比（ORs）或对数相对风险（RRs））时，考虑研究内相关性可提高荟萃分析结果的准确性与效率。Greenland-Longnecker（GL）与Hamling的经典方法通过估计暴露组的伪病例数与非病例数来获取研究内相关性。然而，这两种方法当前可用的实现在简单案例中均可能失效。本文从优化视角重新审视GL与Hamling方法。针对ORs，我们对两种方法分别提出改进方案，确保在任何可行输入下均能收敛。对于GL方法，这一改进通过建立与熵最小化的新关联实现；对于Hamling方法，改进后通过特定初始化可转化为一组可证明可解的等效方程。针对每种方法，我们均提供了保证适用于任何可行输入的实现方案。对于RRs，我们证明新的GL方法始终保证成功，但任何Hamling方法均可能失败：我们给出了无解存在的反例。当报告方差全部相等时，我们推导出保证方法成功的充分条件。