4.3.2 Statistical models for meta-analysis

There are three categories of statistical models for meta-analysis: the fixed effects model, random effects model, and mixed effects models (Hedges 1992). Only the first two models are used in JBI SUMARI for meta-analysis and discussed here. Using the fixed-effect model we assume that the true effect size for all studies is identical and the effect sizes estimated in studies are different only due to errors in estimating the effect size (Borenstein et al 2010). In the random-effects model we assume a distribution of effects, not a common identical effect size, and we assume that the meta-analysis summary effect size is an estimate of the mean of a distribution of true effects, not a common shared effect size identical for all studies (Borenstein et al 2010).

The proposed statistical model for meta-analysis should be explicitly indicated in the review protocol. When considering statistical inference, meta-analysis using the fixed effects model is appropriate if the aim is to draw statistical conclusions only about the studies included in the meta-analysis, and that the random effects model is appropriate whenever statistical generalizations beyond the included studies are considered (Cooper and Hedges 1994). Commonly, review authors want to generalize the conclusions beyond the actual studies included in meta-analysis, therefore we suggest that the default model for meta-analysis in JBI reviews should be the random effects model. However, it has been recommended by statisticians that the fixed effects model is the appropriate model whenever the number of studies is small (less than five studies) (Cooper and Hedges 1994; Murad et al 2015, p.511). Further details about the fixed effects and random effects models for meta-analysis, including a flowchart for the decisions regarding the selection of the meta-analysis model are provided by Tufanaru et al (2015).