Wolfgang Viechtbauer

The purpose of this course is to cover advanced methods for meta-analysis with particular emphasis on using the statistical software R for the analyses. Therefore, course participants should ideally have an understanding of standard meta-analytic techniques and methods (see below for course prerequisites).

We will start out by briefly reviewing standard meta-analytic models (i.e., equal/fixed-effects, random-effects, and meta-regression models), focusing on how to fit and interpret these models in R. This will then be the starting point to delve into more complex data structures that one may encounter in practice and to consider appropriate models for analyzing such data. Models and techniques to be discussed in this context include multilevel and multivariate models, methods for dealing with dependent/correlated outcomes including cluster-robust inference methods (also known as robust variance estimation), arm-based versus contrast-based models, network meta-analysis / mixed treatment comparisons, meta-analysis of diagnostic tests, models with crossed random effects, phylogenetic meta-analysis, spatio-temporal models, and location-scale models. We will also examine the distinction between models that assume normal sampling distributions for the observed outcomes and models that are based on alternative distributional assumptions (e.g., random/mixed-effects (conditional) logistic and Poisson regression models).

Course participants should ideally have an understanding of standard meta-analytic methods and some prior experience with analyzing meta-analytic data. Most importantly, participants should be familiar with the computation and interpretation of outcome measures commonly used in meta-analyses (e.g., risk/odds ratios, risk differences, raw or standardized mean differences, response ratios (ratios of means), raw or Fisher's r-to-z transformed correlations) and the interpretation and application of equal/fixed-effects, random-effects, and meta-regression models. I also offer a more introductory meta-analysis course that covers these and other topics in great detail.

The primary software package to be used during the course for the analyses will be R (see below for more details). Although everything that you need to know to do the computer exercises will be explained in the course, this is not a comprehensive R programming course. Therefore, if you are new to R, it would be useful to familiarize yourself with R a little bit ahead of time (see also my notes on preparing to use R).

Finally, further below, you will find a list of references which describe some of the models and methods that will be discussed during the course. If you have the time and feel very ambitious, it would be ideal to at least skim through them ahead of time in preparation for the course (and to get a better idea of the course contents). But this is not a course prerequisites per se – all of the models and methods will be introduced step-by-step during the course without assuming that you have already read the papers listed below.

The course will be given online via the video conferencing platform Zoom. While it is possible to join the course simply via your browser, I would not recommend this (certain features are not available via the 'web client' and the video/audio quality tends to be poorer). Therefore, I would highly recommend to install the Zoom client (which you can get here).

We will conduct a number of practical exercises throughout the course where we make use of the statistical software package R. Therefore, please download R from the Comprehensive R Archive Network (CRAN). Choose the appropriate "Download R" link depending on your operating system and follow the instructions for downloading and installing R. If you already have R installed, please check that it is the current version (you can check what the 'latest release' of R is by going to CRAN and then compare this with the version shown when you start R). If you do not have the latest version installed, please update.

Although not strictly necessary, it will be useful to also install an integrated development environment (IDE) for R. A popular choice these days is RStudio. So, unless you already have a different setup, please download and install RStudio.

Once R and RStudio are installed, please also install the metafor package (an add-on for conducting meta-analyses with R). More details about the package can be found on the metafor package website. You should be able to install the package by starting R/RStudio and then typing install.packages("metafor") into the 'Console'.

In addition, we are likely to make use of a number of additional packages during the course. You should be able to install all of the needed packages at once with the following command (this may take a few moments to complete):

install.packages(c("clubSandwich", "lme4", "GLMMadaptive", "glmmTMB", "numDeriv", 
                   "minqa", "nloptr", "dfoptim", "ucminf", "lbfgsb3c", "subplex", 
                   "BB", "Rsolnp", "alabama", "optimx", "optimParallel", "sp", "ape"))

At this time, it is not possible to register for the course. The course registration form will be posted as soon as another round of the course is organized.

• The starting time of the course was chosen so that people from Europe, Africa, and Asia (and possibly Australia) can participate in the course without having to be up in the middle of the night (although people far East will need to be up quite late). My apologies to people from North/South America for whom these times are probably not feasible (a future round of the course might run at times more suitable for those from these regions).

• In the 'in person' courses that I teach, I often end up troubleshooting general computer problems for some of the course participants. I will not be able to do this in this course. Therefore, make sure you sort out any problems with installing the necessary software ahead of time.

• The course fee is meant to be paid per person. While I won't take active measures to check if a single person is behind each connection during the course, I appeal to your sense of fairness to register individually.

• The course will not be recorded. By registering, you also agree not to make any recordings of the course on your end.

Berkey, C. S., Hoaglin, D. C., Antczak-Bouckoms, A., Mosteller, F., & Colditz, G. A. (1998). Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine, 17(22), 2537–2550. [link]

Fernández-Castilla, B., Maes, M., Declercq, L., Jamshidi, L., Beretvas, S. N., Onghena, P., & Van den Noortgate, W. (2019). A demonstration and evaluation of the use of cross-classified random-effects models for meta-analysis. Behavior Research Methods, 51(3), 1286-1304. [link]

Gleser, L. J., & Olkin, I. (2009). Stochastically dependent effect sizes. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (2nd ed., pp. 357–376). New York: Russell Sage Foundation.

Ishak, K. J., Platt, R. W., Joseph, L., Hanley, J. A., & Caro, J. J. (2007). Meta-analysis of longitudinal studies. Clinical Trials, 4(5), 525–539. [link]

Jackson, D., Barrett, J. K., Rice, S., White, I. R., & Higgins, J. P. (2014). A design-by-treatment interaction model for network meta-analysis with random inconsistency effects. Statistics in Medicine, 33(21), 3639–3654. [link]

Kalaian, H. A., & Raudenbush, S. W. (1996). A multivariate mixed linear model for meta-analysis. Psychological Methods, 1(3), 227–235. [link]

Konstantopoulos, S. (2011). Fixed effects and variance components estimation in three-level meta-analysis. Research Synthesis Methods, 2(1), 61–76. [link]

Nakagawa, S., & Santos, E. S. A. (2012). Methodological issues and advances in biological meta-analysis. Evolutionary Ecology, 26(5), 1253–1274. [link]

Pustejovsky, J. E., & Tipton, E. (2022). Meta-analysis with robust variance estimation: Expanding the range of working models. Prevention Science, 23, 425–438. [link]

Salanti, G., Higgins, J. P. T., Ades, A. E., & Ioannidis, J. P. A. (2008). Evaluation of networks of randomized trials. Statistical Methods in Medical Research, 17(3), 279–301. [link]

Senn, S., Gavini, F., Magrez, D., & Scheen, A. (2013). Issues in performing a network meta-analysis. Statistical Methods in Medical Research, 22(2), 169–189. [link]

Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87(2), 245–251. [link]

Trikalinos, T. A., & Olkin, I. (2012). Meta-analysis of effect sizes reported at multiple time points: A multivariate approach. Clinical Trials, 9(5), 610–620. [link]

van Houwelingen, H. C., Arends, L. R., & Stijnen, T. (2002). Advanced methods in meta-analysis: Multivariate approach and meta-regression. Statistics in Medicine, 21(4), 589–624. [link]

van Houwelingen, H. C., Zwinderman, K. H., & Stijnen, T. (1993). A bivariate approach to meta-analysis. Statistics in Medicine, 12(24), 2273–2284. [link]

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48. [link]

Viechtbauer, W., & López-López, J. A. (2022). Location-scale models for meta-analysis. Research Synthesis Methods, 13(6), 697–715. [link]