Abstract
We consider six different estimators of residual heterogeneity in random-effects meta-regression, five estimators already known and implemented in the R package metafor and one estimator not yet considered in random-effects meta-regression. In a numerical study, we investigate the properties of these residual heterogeneity estimators as well as the impact of these estimators on the properties of the regression parameter estimates. It turns out that the new estimator performs quite well in terms of bias and mean squared error. The impact of the different residual heterogeneity estimators on the actual confidence coefficient of confidence intervals for regression parameters can be substantially different as shown in the numerical study.
Highlights
Meta-analysis aims to compare and possibly combine estimates of effect across related studies
We investigate the properties of the residual heterogeneity estimators Section 2 and their influence on the regression parameter estimates
For k = 10 studies, restricted maximum likelihood (REML) seems to be perform best followed by MP and DL, where DL is negatively biased for large τ2 and MP positively biased for larger τ2
Summary
Meta-analysis aims to compare and possibly combine estimates of effect across related studies. In a meta-analysis of clinical trials, the overall effect of a treatment can be expressed as standardized difference of means for normal responses or as relative risk or odds ratio for binary responses. Methods for providing such an overall estimate are well known[1,2]. In randomeffects meta-regression inference, that is, in a metaregression model allowing for residual heterogeneity, accurate estimation of the variances of the parameter estimates is fundamental, as always in statistical inference. The outline of this paper is as follows: Section 2 contains the description of the general randomeffects meta-regression model and the residual heterogeneity estimators. For a quadratic matrix A, let |A| denote the determinant of A and tr(A) the trace of A. 1k is the k-dimensional vector consisting of ones
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