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Specifically, we found that different estimates for pooled effects, standard errors, between-study heterogeneity and correlation between random effects can result from choosing a different method (one-stage or two-stage), choosing a different estimation procedure (MLE, REML, MOM, number of quadrature points) and choosing a different model specification (independent random effects, joint random effects, stratified estimation).
Although these differences were usually not substantial, in the DVT example they lead to discrepancies concerning the statistical significance of age, duration of symptoms, family history of thrombofilia, presence of erythema, presence of paresis and (dichotomized) D-dimer value. This makes it desirable to pre-specify in a study protocol what meta-analysis method will be used, to avoid unjustified post-hoc analyses being performed to achieve statistical significance.
We generally recommend that the one-stage method should be used.