Information about the statistical techniques available in RevMan is addressed in section 9.4 of the Cochrane Handbook for Systematic Reviews of Interventions and you should read it now.
In order to choose the method you are going to use in your meta-analysis, the first concept to understand is the difference between a fixed effect model and a random effects model.
What does 'fixed effect' mean?
To come up with any statistical model, or method for meta-analysis, we first need to make some assumptions. It is these assumptions that form the differences between all the methods listed above.
A fixed effect model of meta-analysis is based on a mathematical assumption that every study is evaluating a common treatment effect. That means the effect of treatment, allowing for the play of chance, was the same in all studies. Another way of explaining this is to imagine that if all the studies were infinitely large they'd give identical results.
The summary treatment effect estimate resulting from this method of meta-analysis is this one 'true' or 'fixed' treatment effect, and the confidence interval describes how uncertain we are about the estimate.
Sometimes this underlying assumption of a fixed effect meta-analysis (i.e. that diverse studies can be estimating a single effect) is too simplistic. Therefore, the alternative approaches to meta-analysis are (i) to try to explain the variation or (ii) to use a random effects model.
Random effects meta-analyses (DerSimonian and Laird)
As we discussed above, fixed effect meta-analysis assumes that there is one identical true treatment effect common to every study.The random effects model of meta-analysis is an alternative approach to meta-analysis that does not assume that a common ('fixed') treatment effect exists. The random effects model assumes that the true treatment effects in the individual studies may be different from each other. That means there is no single number to estimate in the meta-analysis, but a distribution of numbers. The most common random effects model also assumes that these different true effects are normally distributed. The meta-analysis therefore estimates the mean and standard deviation of the different effects.
By selecting 'random effects' in the analysis part of RevMan you can calculate an odds ratio, risk ratio or a risk difference based on this approach.
The Mantel-Haenszel approach
The Mantel-Haenszel approach was developed by Mantel and Haenszel over 40 years ago to analyse odds ratios, and has been extended by others to analyse risk ratios and risk differences. It is unnecessary to understand all the details, but is sufficient to say that the Mantel-Haenszel method assumes a fixed effect and combines studies using a method similar to inverse variance approaches to determine the weight given to each study.
The Peto method
The Peto method works for odds ratios only. Focus is placed on the observed number of events in the experimental intervention. We call this O for 'observed' number of events, and compare this with E, the 'expected' number of events. Hence an alternative name for this method is the 'O - E' method. The expected number is calculated using the overall event rate in both the experimental and control groups. Because of the way the Peto method calculates odds ratios, it is appropriate when trials have roughly equal number of participants in each group and treatment effects are small. Indeed, it was developed for use in mega-trials in cancer and heart disease where small effects are likely, yet very important.
The Peto method is better than the other approaches at estimating odds ratios when there are lots of trials with no events in one or both arms. It is the best method to use with rare outcomes of this type.
The Peto method is generally less useful in Cochrane reviews, where trials are often small and some treatment effects may be large.