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arXiv · 2609.19211

An absolute measure of heterogeneity for lnOR in meta-analysis

Ke Yang·Lei Shi·Wangli Xu·Liping Zhu·Tiejun Tong
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Abstract

Quantifying the heterogeneity is an important issue in meta-analysis. The conventional heterogeneity statistic, $I^2$, heavily depends on study sample sizes and tends to approach one as the sample sizes increase. To overcome this limitation, a sample size independent measure, ${\rm ICC}_{\rm MA}$, has recently been developed to quantify the heterogeneity, yet this method is restricted to meta-analysis with continuous outcomes. In practice, however, binary outcomes are more widely encountered, with the log odds ratio (lnOR) frequently adopted as an effect size to compare the effects of two treatments in terms of odds. To fill the gap, we propose a new heterogeneity measure for meta-analysis with binary outcomes by introducing a latent continuous variable model. Under this framework, the proposed measure admits a closed-form expression within the random-effects meta-analysis model with lnOR as the effect size. We define this sample size independent measure as ${\rm ICC}_{\rm MA}^{\rm OR}$, and moreover propose a new estimator, $I^2_A$, to evaluate this measure. Simulation studies demonstrate that our new estimator is nearly unbiased and aligns closely with its counterpart applied for standardized mean differences when the continuous variable is observable. A real data application further demonstrates that the proposed heterogeneity statistic for binary outcomes and its counterpart for continuous outcomes provide interpretable and coherent estimates across different outcome types.

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Ke Yang, Lei Shi, Wangli Xu, Liping Zhu, Tiejun Tong. 2026-09-16. An absolute measure of heterogeneity for lnOR in meta-analysis. https://arxiv.org/abs/2609.19211

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