Meta-analysis is the combined statistical analysis of the results of several studies, with the aim of obtaining clearer or firmer conclusions than can be obtained by considering them individually. When possible, meta-analysis should be performed on the basis of the individual observations used in each study.
In a fixed-effect meta-analysis, it is assumed that the true treatment effect is the same in every study. However, treatment effects may vary between studies, and it is then natural to regard the studies as a random sample, leading to a random-effect meta-analysis.
The main effect of treatment may be partitioned into a between-study and a within-study component. When the studies are randomized experiments (e.g. clinical trials), it is considered prudent to interpret only the within-study component. This is because the between-studies component may be biased by confounding with other variables, whereas the within-studies component is defended against such bias by the randomization process.
The within-studies estimate of the treatment effect may be obtained without explicit partitioning, by specifying study and treatment as fixed-effect terms, but the study × treatment interaction as a random-effect term. This is an exception to the rule that the interaction between two fixed-effect terms is also fixed (see Section 6.3).
When a random-effect meta-analysis is performed, shrunk estimates of the treatment effects in individual studies may be obtained.
Although meta-analysis ...