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：元分析能够严格整合多项研究的估计值及其不确定性。当某项研究跨暴露组报告多个估计值（如对数比值比或对数相对风险）时，考虑研究内相关性可提升元分析结果的准确性和效率。Greenland-Longnecker和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，现有这两种方法的实现方式在简单案例中均会失效。我们从优化视角回顾了GL与Hamling方法。针对比值比，我们为每种方法提供了确保任意可行输入均能收敛的修正方案：对于GL方法，通过建立与熵最小化的新关联实现；对于Hamling方法，通过引入特定初始化条件下可证明可解的等价方程组实现。我们为每种方法提供了保证在任意可行输入下均可运行的实现代码。针对相对风险，我们证明新GL方法总能成功收敛，但任何Hamling方法均可能失败：我们给出了解不存在的反例。当报告方差相同时，我们推导出保证相对风险方法成功的充分条件。