Simulation study of estimating between-study variance and overall effect in meta-analyses of log-response-ratio for lognormal data

Methods for random-effects meta-analysis require an estimate of the between-study variance, $τ^2$. The performance of estimators of $τ^2$ (measured by bias and coverage) affects their usefulness in assessing heterogeneity of study-level effects, and also the performance of related estimators of the overall effect. For the effect measure log-response-ratio (LRR, also known as the logarithm of the ratio of means, RoM), we review four point estimators of $τ^2$ (the popular methods of DerSimonian-Laird (DL), restricted maximum likelihood, and Mandel and Paule (MP), and the less-familiar method of Jackson), four interval estimators for $τ^2$ (profile likelihood, Q-profile, Biggerstaff and Jackson, and Jackson), five point estimators of the overall effect (the four related to the point estimators of $τ^2$ and an estimator whose weights use only study-level sample sizes), and seven interval estimators for the overall effect (four based on the point estimators for $τ^2$, the Hartung-Knapp-Sidik-Jonkman (HKSJ) interval, a modification of HKSJ that uses the MP estimator of $τ^2$ instead of the DL estimator, and an interval based on the sample-size-weighted estimator). We obtain empirical evidence from extensive simulations of data from lognormal distributions.