Chapter 4 Pooling Effect Sizes
Now, let us get to the core of every meta-analysis: pooling your effect sizes to get one overall effect size estimate of the studies.
When pooling effect sizes in Meta-Analysis, there are two approaches which we can use: the Fixed-Effect Model, or the Random-Effects Model (Borenstein et al. 2011). There is an extensive debate on which model fits best in which context (Fleiss 1993), with no clear consensus in sight. Although it has been recommended to only resort to the random-effects pooling model in clinical psychology and the health sciences (Cuijpers 2016), we will describe how to conduct both in R here.
Both of these models only require an effect size, and a dispersion (variance) estimate for each study, of which the inverse is taken. This is why the methods are often called generic inverse-variance methods.
We will describe in-depth how to conduct meta-analyses in R with effect sizes based on continuous outcome data (such as standardized mean differences) first, as these are the most common ones in psychology and the health science field. Later on, we will extend this knowledge to meta-analyses with binary outcome data, which might be important if you are focusing on prevention trials.
Borenstein, Michael, Larry V Hedges, Julian PT Higgins, and Hannah R Rothstein. 2011. Introduction to Meta-Analysis. John Wiley & Sons.
Fleiss, JL. 1993. “Review Papers: The Statistical Basis of Meta-Analysis.” Statistical Methods in Medical Research 2 (2). Sage Publications Sage CA: Thousand Oaks, CA: 121–45.
Cuijpers, Pim. 2016. “Meta-Analyses in Mental Health Research. A Practical Guide.” Amsterdam, the Netherlands: Pim Cuijpers Uitgeverij.
Schwarzer, Guido. 2007. “Meta: An R Package for Meta-Analysis.” R News 7 (3): 40–45.