Cochran's $Q$ statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value (under an incorrect null distribution) is part of several popular estimators of the between-study variance, $\tau^2$. Those applications generally do not account for the studies' use of estimated variances in the inverse-variance weights that define $Q$ (more explicitly, $Q_{IV}$). Importantly, those weights make approximating the distribution of $Q_{IV}$ rather complicated. As an alternative, we are investigating a $Q$ statistic, $Q_F$, whose constant weights use only the studies' arm-level sample sizes. For log-odds-ratio, log-relative-risk, and risk difference as the measure of effect, these simulations study approximations to the distributions of $Q_F$ and $Q_{IV}$, as the basis for tests of heterogeneity. We present the results in 132 Figures, 153 pages in total.

翻译：摘要：Cochran's $Q$ 统计量常用于元分析中的异质性检验。其期望值（基于错误的零假设分布）是若干常用研究间方差 $\tau^2$ 估计量的组成部分。通常情况下，这些应用并未考虑研究在定义 $Q$ 的逆方差权重（更具体地表示为 $Q_{IV}$）中使用估计方差的影响。重要的是，这些权重使得 $Q_{IV}$ 分布的近似变得相当复杂。作为替代方案，我们研究了一种常数权重的 $Q$ 统计量 $Q_F$，其权重仅使用研究的组别样本量。以对数优势比、对数相对风险和风险差作为效应量指标，本研究模拟了 $Q_F$ 和 $Q_{IV}$ 分布的近似方法，并据此作为异质性检验的基础。我们以132张图表、共153页篇幅呈现结果。