Pitfalls of using the risk ratio in meta‐analysis

Ilyas Bakbergenuly, David Hoaglin, Elena Kulinskaya

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)
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For meta-analysis of studies that report outcomes as binomial proportions, the most popular measure of effect is the odds ratio (OR), usually analyzed as log(OR). Many meta-analyses use the risk ratio (RR) and its logarithm, because of its simpler interpretation. Although log(OR) and log(RR) are both unbounded, use of log(RR) must ensure that estimates are compatible with study-level event rates in the interval (0, 1). These complications pose a particular challenge for random-effects models, both in applications and in generating data for simulations. As background we review the conventional random-effects model and then binomial generalized linear mixed models (GLMMs) with the logit link function, which do not have these complications. We then focus on log-binomial models and explore implications of using them; theoretical calculations and simulation show evidence of biases. The main competitors to the binomial GLMMs use the beta-binomial (BB) distribution, either in BB regression or by maximizing a BB likelihood; a simulation produces mixed results. Two examples and an examination of Cochrane meta-analyses that used RR suggest bias in the results from the conventional inverse-variance-weighted approach. Finally, we comment on other measures of effect that have range restrictions, including risk difference, and outline further research.
Original languageEnglish
Pages (from-to)398-419
Number of pages22
JournalResearch Synthesis Methods
Issue number3
Early online date10 Mar 2019
Publication statusPublished - Sep 2019


  • Relative risk, risk difference, response ratio, log-binomial model, beta-binomial model

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