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# 3.3.6 Meta-analysis: Statistical Methods

Different statistical methods are available for meta-analysis: Mantel-Haenszel method, Peto’s method, DerSimonian and Laird method, and the inverse variance method. The Mantel-Haenszel method, the Peto’s method, and the inverse variance method are methods used with the fixed effects model of meta-analysis (Deeks et al 2008). The DerSimonian and Laird method is used with the random effects model of meta-analysis (Deeks et al 2008).

The inverse variance method may be used with all types of ratios and differences for example the log odds ratio, log relative risk, risk difference, mean difference (weighted mean difference) and standardized mean difference (Petitti 2000; Deeks et al 2008). The Mantel–Haenszel method may be used with ratios, typically with odds ratio, but can be applied to rate ratio and risk ratio (Petitti 2000). The Peto’s method is used with odds ratios (Petitti 2000). DerSimonian and Laird method may be used with all types of ratios (odds ratio, risk ratio) and difference (weighted mean difference) and standardized mean difference (Petitti 2000; Deeks et al 2008).

There are different statistical methods (formulae) used to compute a standardized mean difference for each study including the Hedges’ method, the Cohen’s method, and the Glass method. If a fixed effects model is used for meta-analysis of standardized mean differences then the inverse variance method of meta-analysis may be used. If a random effects model is used for meta-analysis of standardized mean differences then the DerSimonian and Laird method may be used.

When deciding what method for meta-analysis to be used statistical considerations are important. When studies have small sample sizes and the number of events is small in these studies the inverse variance method may not be appropriate; in these circumstances, it may be preferable to use the Mantel-Haenszel method (Deeks et al 2008). Peto’s method may produce serious under-estimates when the odds ratio is far from unity (large treatment effects) (Sutton et al 2000). If the number of studies to be combined is small, but the within-study sample sizes per study are large, the inverse-weighted method should be used (Sutton et al 2000, p.69). If there are many studies to combine, but the within-study sample size in each study is small, the Mantel-Haenszel method is preferred (Sutton et al 2000).