  Methods for random-effects meta-analysis require an estimate of the
between-study variance, $\tau^2$. The performance of estimators of $\tau^2$
(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 $\tau^2$ (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 $\tau^2$ (profile likelihood,
Q-profile, Biggerstaff and Jackson, and Jackson), five point estimators of the
overall effect (the four related to the point estimators of $\tau^2$ 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
$\tau^2$, the Hartung-Knapp-Sidik-Jonkman (HKSJ) interval, a modification of
HKSJ that uses the MP estimator of $\tau^2$ 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.
