Methodology

Aggregation of results

We use two different approaches to aggregate the results from the different studies included in the meta-analysis: a fixed effects model and a random effects model.

Fixed effects model

A so-called 'fixed effects model' is probably the simplest version of calculating meta-estimates. It uses the 'inverse-variance method' to calculate the weighted average of the included studies as:

A so-called 'fixed effects model' is probably the simplest version of calculating meta-estimates. It uses the 'inverse-variance method' to calculate the weighted average of the included studies as:

where is the estimated effect size from the study, is the weight assigend to study and the summation is across all studies. In the fixed effects model,

with being the standard error of study .

This type of analysis assumes that all effect estimates are estimating the same underlying effect. More information: Borenstein, M.; Hedges, L.; Higgins, J.; Rothstein, H (2009): A basic introduction to fixed-effect and random-effects models for meta-analysis

Random effects model

Random effects models are a variation of the 'inverse-variance method' that is also used in fixed effects models. However, they operate on the assumption that the different studies included in the meta-analysis estimate different but related effects.

The general formula for calculating the aggregated effect estimate is the same as in the fixed effects model:

where is the estimated effect size from the study, is the weight assigend to study and the summation is across all studies.

However, the weights of the studies take into account the between-study variance :

You can find information on how to calculate (T^2 ) in: Borenstein, M.; Hedges, L.; Higgins, J.; Rothstein, H (2009): A basic introduction to fixed-effect and random-effects models for meta-analysis