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Background  Analyses of multicenter studies often need to account for center clustering to ensure valid inference. For binary outcomes, it is particularly challenging to properly adjust for center when the number of centers or total sample size is small, or when there are few events per center. Our objective was to evaluate the performance of generalized estimating equation (GEE) log-binomial and Poisson models, generalized linear mixed models (GLMMs) assuming binomial and Poisson distributions, and a Bayesian binomial GLMM to account for center effect in these scenarios.    Methods  We conducted a simulation study with few centers (≤30) and 50 or fewer subjects per center, using both a randomized controlled trial and an observational study design to estimate relative risk. We compared the GEE and GLMM models with a log-binomial model without adjustment for clustering in terms of bias, root mean square error (RMSE), and coverage. For the Bayesian GLMM, we used informative neutral priors that are skeptical of large treatment effects that are almost never observed in studies of medical interventions.    Results  All frequentist methods exhibited little bias, and the RMSE was very similar across the models. The binomial GLMM had poor convergence rates, ranging from 27% to 85%, but performed well otherwise. The results show that both GEE models need to use small sample corrections for robust SEs to achieve proper coverage of 95% CIs. The Bayesian GLMM had similar convergence rates but resulted in slightly more biased estimates for the smallest sample sizes. However, it had the smallest RMSE and good coverage across all scenarios. These results were very similar for both study designs.    Conclusions  For the analyses of multicenter studies with a binary outcome and few centers, we recommend adjustment for center with either a GEE log-binomial or Poisson model with appropriate small sample corrections or a Bayesian binomial GLMM with informative priors.    Electronic supplementary material  The online version of this article (doi:10.1186/s13063-017-2248-1) contains supplementary material, which is available to authorized users.

Estimating relative risks in multicenter studies with a small number of centers — which methods to use? A simulation study