Validity of regression meta-analyses versus pooled analyses of mixed effect linear models

Abstract

Meta-analysis is a class of techniques for combining the results of many small studies to reach a unified inference for a parameter of interest, for example a parameter quantifying treatment effectiveness. Often, the statistician has from each individual study only an estimator of the parameter of interest, together with an estimator of standard error, and the separate estimates are treated as data and fitted within a so-called `meta-regression' model, with study as a categorical predictor and the parameter of interest regarded as a common mean, and with error term consisting of a constant-variance error plus an independent study effect with standard deviation equal to the separate estimated study standard error. Occasionally, patient-level data including covariates are available from all of the component studies, in which case a pooled patient-level analysis can be conducted including fixed covariate effects, plus study effects as random intercepts, and possibly also including random treatment-by-study interactions. Comparisons are sometimes published in biomedical settings between the meta-analysis results and the results of pooled mixed (generalized) linear model analyses. This paper reports theoretical and simulation results regarding the biases of meta-analysis estimates versus pooled model estimates when the latter are correct, showing that in {\it linear\/} models, these biases are generally small, especially when treatment-allocation is balanced and covariate and error distributions are symmetric.