A comparison of 7 random-effects models for meta-analyses that estimate the summary odds ratio

Comparative trials that report binary outcome data are commonly pooled in systematic reviews and meta-analyses. This type of data can be presented as a series of 2-by-2 tables. The pooled odds ratio is often presented as the outcome of primary interest in the resulting meta-analysis. We examine the use of 7 models for random-effects meta-analyses that have been proposed for this purpose. The first of these models is the conventional one that uses normal within-study approximations and a 2-stage approach. The other models are generalised linear mixed models that perform the analysis in 1 stage and have the potential to provide more accurate inference. We explore the implications of using these 7 models in the context of a Cochrane Review, and we also perform a simulation study. We conclude that generalised linear mixed models can result in better statistical inference than the conventional 2-stage approach but also that this type of model presents issues and difficulties. These challenges include more demanding numerical methods and determining the best way to model study specific baseline risks. One possible approach for analysts is to specify a primary model prior to performing the systematic review but also to present the results using other models in a sensitivity analysis. Only one of the models that we investigate is found to perform poorly so that any of the other models could be considered for either the primary or the sensitivity analysis.