Multilevel models for meta-analysis, and their application to absolute risk differences

Meta-analysis can be considered a multilevel statistical problem, since information within studies is combined in the presence of potential heterogeneity between studies. Here a general multilevel model framework is developed for meta-analysis to combine either summary data or individual patient outcome data from each study, and to include either study or individual level covariates that might explain heterogeneity. Classical and Bayesian approaches to estimation are contrasted. These methods are applied to a meta-analysis of trials of thrombolytic therapy after myocardial infarction. Subgroups within the trials were available, categorized by the time delay until treatment, so that a three-level random effects model that includes time delay as a covariate is proposed. In addition it was desired to represent the treatment effect as an absolute risk reduction, rather than the conventional odds ratio. We show how this can be achieved within a Bayesian analysis, while still recognizing the binary nature of the original outcome data.