Summary
Background: The random-effects (RE) model is the standard choice for meta-analysis in the presence
of heterogeneity, and the stand ard RE method is the DerSimonian and Laird (DSL) approach,
where the degree of heterogeneity is estimated using a moment-estimator. The DSL approach
does not take into account the variability of the estimated heterogeneity variance
in the estimation of Cochran’s Q. Biggerstaff and Jackson derived the exact cumulative distribution function (CDF)
of Q to account for the variability of Ť 2.
Objectives: The first objective is to show that the explicit numerical computation of the density
function of Cochran’s Q is not required. The second objective is to develop an R package with the possibility
to easily calculate the classical RE method and the new exact RE method.
Methods: The novel approach was validated in extensive simulation studies. The different approaches
used in the simulation studies, including the exact weights RE meta-analysis, the
I 2 and T 2 estimates together with their confidence intervals were implemented in the R package
metaxa.
Results: The comparison with the classical DSL method showed that the exact weights RE meta-analysis
kept the nominal type I error level better and that it had greater power in case of
many small studies and a single large study. The Hedges RE approach had inflated type
I error levels. Another advantage of the exact weights RE meta-analysis is that an
exact confidence interval for T 2is readily available. The exact weights RE approach had greater power in case of few
studies, while the restricted maximum likelihood (REML) approach was superior in case
of a large number of studies. Differences between the exact weights RE meta-analysis
and the DSL approach were observed in the re-analysis of real data sets. Application
of the exact weights RE meta-analysis, REML, and the DSL approach to real data sets
showed that conclusions between these methods differed.
Conclusions: The simplification does not require the calculation of the density of Cochran’s Q, but only the calculation of the cumulative distribution function, while the previous
approach required the computation of both the density and the cumulative distribution
function. It thus reduces computation time, improves numerical stability, and reduces
the approximation error in meta-analysis. The different approaches, including the
exact weights RE meta-analysis, the I 2 and T 2estimates together with their confidence intervals are available in the R package
metaxa, which can be used in applications.
Keywords
Cochran’s
Q
- DerSimonian and Laird - exact weights - random-effects - meta-analysis -
I 2
- T
2
