*Jonathan J. Deeks, Richard D. Riley, Julian P.T. Higgins*

**Abstract**

Meta-analysis of controlled trials is usually a two-stage process involving the calculation of an appropriate summary statistic of the intervention effect for each trial, followed by the combination of these statistics into a weighted average. Two models for meta-analysis are in widespread use. A fixed-effect meta-analysis (also known as common-effect meta-analysis) assumes that the intervention effect is the same in every trial. A random-effects meta-analysis additionally incorporates an estimate of between-trial variation of the intervention effect (heterogeneity) into the calculation of the weighted average, providing a summary effect that is the best estimate of the average intervention effect of a distribution of possible intervention effects. Selection of a meta-analysis method for a particular analysis should reflect the data type, choice of summary statistic (considering the consistency of the effect and ease of interpretation of the statistic), and expected heterogeneity, and the known limitations of the computational methods.

In this chapter we consider the general principles of meta-analysis, and introduce the most commonly used methods for performing meta-analysis. We shall focus on meta-analysis of randomized trials evaluating the effects of an intervention, but much the same principles apply to other comparative studies, notably case–control and cohort studies evaluating risk factors. An important first step in a systematic review of controlled trials is the thoughtful consideration of whether it is appropriate to combine all (or perhaps some) of the trials in a meta-analysis, to yield an overall statistic (together with its confidence interval) that summarizes the effect of the intervention of interest. Decisions regarding the “combinability” of results should largely be driven by consideration of the similarity of the trials (in terms of participants, experimental and comparator interventions, and outcomes), but statistical investigation of the degree of variation between individual trial results, which is known as heterogeneity, can also contribute.

**Corrections**

On table 9.3, the last prediction interval should be (-0.18, 0.08).

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**Author affiliations**

*Jonathan G. Deeks*

*Jonathan G. Deeks*

Test Evaluation Research Group, Institute of Applied Health Research, University of Birmingham, Birmingham, UK

*Richard D. Riley*

*Richard D. Riley*

Centre for Prognosis Research, School of Medicine, Keele University, Newcastle-under-Lyme, UK

*Julian P.T. Higgins*

*Julian P.T. Higgins*

Population Health Sciences, Bristol Medical School, University of Bristol, Bristol, UK

National Institute of Health Research, Applied Research Collaboration West, University Hospital Bristol and Weston NHS Foundation Trust, Bristol, UK

**How to cite this chapter?**

*For the printed version of the book*

*For the printed version of the book*

Deeks, J.J., Riley, R.D. and Higgins, J.P.T. (2022). Chapter 9. Combining results using meta-analysis. In: *Systematic Reviews in Health Research: Meta-analysis in Context* (eds M. Egger, J.P.T. Higgins and G. Davey Smith), pp 159-184. Hoboken, NJ : Wiley.

*For the electronic version of the book*

*For the electronic version of the book*

Deeks, J.J., Riley, R.D. and Higgins, J.P.T. (2022). Chapter 9. Combining results using meta-analysis. In: *Systematic Reviews in Health Research: Meta-analysis in Context* (eds M. Egger, J.P.T. Higgins and G. Davey Smith). https://doi.org/10.1002/9781119099369.ch9