Chapter 5 Pooling Effect Sizes
Now, let’s 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 basic approaches: the Fixed-Effect-Model, or the Random-Effects-Model (Borenstein et al. 2011). The fixed effect model assumes that one true effect size exists in the population; the random effects model assumes that the true effect varies (and is normally distributed). 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 continuous variables (such as effect sizes), as these are the most common ones in psychology and the health science field. Later on, we will present briefly how to do meta-analyses with binary outcome data too, which might be important if you’re focusing on prevention trials.
For these meta-analyses, we’ll use the metafor package (Viechtbauer and others 2010). In Section 2.1, we showed how to install the package. We load a different package: The metaforest package, which in turn loads the metafor package, and contains the example data for this tutorial.
library(metaforest)References
Borenstein, Michael, Larry V Hedges, Julian PT Higgins, and Hannah R Rothstein. 2011. Introduction to Meta-Analysis. John Wiley & Sons.
Cuijpers, Pim. 2016. “Meta-Analyses in Mental Health Research. A Practical Guide.” Amsterdam, the Netherlands: Pim Cuijpers Uitgeverij.
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.
Viechtbauer, Wolfgang, and others. 2010. “Conducting Meta-Analyses in R with the Metafor Package.” J Stat Softw 36 (3): 1–48.