Simulations for estimation of heterogeneity variance $\tau^2$ in constant and inverse variance weights meta-analysis of log-odds-ratios

TL;DR

This paper introduces new estimators for the heterogeneity variance in meta-analysis of log-odds-ratios, comparing their bias and coverage through extensive simulations against existing methods.

Contribution

It proposes novel point and interval estimators of $ au^2$ based on the $Q$ statistic with effective-sample-size weights, and evaluates their performance.

Findings

New estimators show improved bias and coverage in simulations.

Comparison with existing estimators highlights advantages of the new methods.

Simulation results demonstrate robustness across different scenarios.

Abstract

A number of popular estimators of the between-study variance, $\tau^2$, are based on the Cochran's $Q$ statistic for testing heterogeneity in meta analysis. We introduce new point and interval estimators of $\tau^2$ for log-odds-ratio. These include new DerSimonian-Kacker-type moment estimators based on the first moment of $Q_F$, the $Q$ statistic with effective-sample-size weights, and novel median-unbiased estimators. We study, by simulation, bias and coverage of these new estimators of $\tau^2$ and, for comparative purposes, bias and coverage of a number of well-known estimators based on the $Q$ statistic with inverse-variance weights, $Q_{IV}$, such as the Mandel-Paule, DerSimonian-Laird, and restricted-maximum-likelihood estimators, and an estimator based on the Kulinskaya-Dollinger (2015) improved approximation to $Q_{IV}$.