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### 9.4.2Principles of meta-analysis

All commonly-used methods for meta-analysis follow the following basic principles.

1. Meta-analysis is typically a two-stage process. In the first stage, a summary statistic is calculated for each study, to describe the observed intervention effect. For example, the summary statistic may be a risk ratio if the data are dichotomous or a difference between means if the data are continuous.

2. In the second stage, a summary (pooled) intervention effect estimate is calculated as a weighted average of the intervention effects estimated in the individual studies. A weighted average is defined as where Yi is the intervention effect estimated in the ith study, Wi is the weight given to the ith study, and the summation is across all studies. Note that if all the weights are the same then the weighted average is equal to the mean intervention effect. The bigger the weight given to the ith study, the more it will contribute to the weighted average. The weights are therefore chosen to reflect the amount of information that each study contains. For ratio measures (OR, RR, etc), Yi is the natural logarithm of the measure.

3. The combination of intervention effect estimates across studies may optionally incorporate an assumption that the studies are not all estimating the same intervention effect, but estimate intervention effects that follow a distribution across studies. This is the basis of a random-effects meta-analysis (see Section 9.5.4). Alternatively, if it is assumed that each study is estimating exactly the same quantity a fixed-effect meta-analysis is performed.

4. The standard error of the summary (pooled) intervention effect can be used to derive a confidence interval, which communicates the precision (or uncertainty) of the summary estimate, and to derive a P value, which communicates the strength of the evidence against the null hypothesis of no intervention effect.

5. As well as yielding a summary quantification of the pooled effect, all methods of meta-analysis can incorporate an assessment of whether the variation among the results of the separate studies is compatible with random variation, or whether it is large enough to indicate inconsistency of intervention effects across studies (see Section 9.5).