Statistical models for meta-analysis: A brief tutorial.

Aggregate data meta-analysis is currently the most commonly used method for combining the results from different studies on the same outcome of interest. In this paper, we provide a brief introduction to meta-analysis, including a description of aggregate and individual participant data meta-analysis. We then focus the rest of the tutorial on aggregate data meta-analysis. We start by first describing the difference between fixed and random-effects meta-analysis, with particular attention devoted to the latter. This is followed by an example using the random-effects, method of moments approach and includes an intercept-only model as well as a model with one predictor. We then describe alternative random-effects approaches such as maximum likelihood, restricted maximum likelihood and profile likelihood as well as a non-parametric approach. A brief description of selected statistical programs available to conduct random-effects aggregate data meta-analysis, limited to those that allow both an intercept-only as well as at least one predictor in the model, is given. These descriptions include those found in an existing general statistics software package as well as one developed specifically for an aggregate data meta-analysis. Following this, some of the disadvantages of random-effects meta-analysis are described. We then describe recently proposed alternative models for conducting aggregate data meta-analysis, including the varying coefficient model. We conclude the paper with some recommendations and directions for future research. These recommendations include the continued use of the more commonly used random-effects models until newer models are more thoroughly tested as well as the timely integration of new and well-tested models into traditional as well as meta-analytic-specific software packages.