Interpretation of random effects meta-analysesBMJ 2011; 342 doi: https://doi.org/10.1136/bmj.d549 (Published 10 February 2011) Cite this as: BMJ 2011;342:d549
- Richard D Riley, senior lecturer in medical statistics1,
- Julian P T Higgins, senior statistician2,
- Jonathan J Deeks, professor of biostatistics1
- 1Department of Public Health, Epidemiology and Biostatistics, Public Health Building, University of Birmingham, Birmingham B15 2TT, UK
- 2MRC Biostatistics Unit, Institute of Public Health, Cambridge CB2 0SR, UK
- Correspondence to: R D Riley
- Accepted 11 November 2010
Meta-analysis is used to synthesise quantitative information from related studies and produce results that summarise a whole body of research.1 A typical systematic review uses meta-analytical methods to combine the study estimates of a particular effect of interest and obtain a summary estimate of effect.2 For example, in a meta-analysis of randomised trials comparing a new treatment with placebo, researchers will collect the estimates of treatment effect for each study, as measured by a relevant statistic such as a risk ratio, and then statistically synthesise them to obtain a summary estimate of the treatment effect.
Meta-analyses use either a fixed effect or a random effects statistical model. A fixed effect meta-analysis assumes all studies are estimating the same (fixed) treatment effect, whereas a random effects meta-analysis allows for differences in the treatment effect from study to study. This choice of method affects the interpretation of the summary estimates. We examine the differences and explain why a prediction interval can provide a more complete summary of a random effects meta-analysis than is usually provided.
Difference between fixed effect and random effects meta-analyses
Figure 1⇓ shows two hypothetical meta-analyses, in which estimates of treatment effect are computed and synthesised from 10 studies of the same antihypertensive drug. Each study provides an unbiased estimate of the standardised mean difference in change in systolic blood pressure between the treatment group and the control group. Negative estimates indicate a greater blood pressure reduction for patients in the treatment group than the control group.