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 的 Q 统计量经常用于测试 meta 分析中的异质性。它的期望值(在不正确的零分布下)是 $\tau^2$ 估计量中多个流行方法之一。这些应用通常不考虑研究使用估计方差在反比权重中,这定义了 $Q$(更明确地说,$Q_{IV}$)。重要的是,这些权重使得近似 $Q_{IV}$ 的分布变得相当复杂。作为替代,我们正在研究一个统计量 $Q_F$,它的常数权重只使用研究的臂级样本大小。对于以 log-odds-ratio、log-relative-risk 和风险差异为效应度量的情况,这些模拟研究研究了对 $Q_F$ 和 $Q_{IV}$ 的近似分布,作为异质性检验的基础。我们将结果用132个图表,总共153页的方式呈现。