Meta-analysis in R can be done by using metafor-package, which can be downloaded from the R-project packages site. This package can be used to calculate effect sizes or results and measurements most commonly used in meta-analysis such as risk differences, risk ratios, odds ratios, standardized mean differences, Fisher’s z-transformed correlation coefficients.
Effect size refers to the measure of the strength of the relationship or difference between two variables in a statistical population.
Risk differences compare risks in relative terms i.e. risk of one group minus the risk in other group. In simple terms, risk difference shows the decrease in risk of a given activity or treatment in relation to a control activity or treatment.
Risk ratio is the relative risk that represents the comparison of the risk of any health related event in two groups. It shows the probability of the event occurring in the exposed group vs. unexposed group.
Odds represent the ratio of the probable occurrence of the event versus probability of the non-occurrence of the event. Odds ratio states the ratio of odds, i.e. ratio of odds of an event occurring in the exposed group versus the unexposed group.
After calculation of such measurements in meta-analysis, the metafor package allows the user to fit fixed-, random-, and mixed-effects models to these data. Moreover, “meta-regression” analysis can be carried out by the inclusion of study-level covariates (‘moderators’) in these models.
Fixed-effects model shows the observed quantities in terms of explanatory variables that are treated if the quantities were non-random. Random-effects model shows that the dataset being analysed consists of a hierarchy of different populations whose differences related to that hierarchy.
The Mantel-Haenszel and Peto’s method can also be implemented for meta-analysis of 2×2 table data.
The Mantel-Haenszel method is the most popular method for calculation of a weighted risk ratio or odds ratios. Peto’s method is also a method of combining odds ratios.