Abstract
BackgroundAnalyses 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.MethodsWe 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.ResultsAll 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.ConclusionsFor 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.
Highlights
Analyses of multicenter studies often need to account for center clustering to ensure valid inference
Convergence For the Bayesian models, trace plots of the parameters showed the three chains mixing well after burn-in, except for a small percentage of the datasets, where one of the Markov chain Monte Carlo (MCMC) chains of σ failed to converge near 0 for a portion of the chain. (Other parameters did not converge; an example of an Randomized controlled trial (RCT) dataset is shown in Additional file 1: Figure S1.) These convergence issues were detected by the R diagnostic (>1.1), and these datasets were excluded from the results
Convergence rates for Bayesian models ranged from 92% for the RCT scenario with 4 centers and 10 subjects per center to 100% for some scenarios with 10 or 30 centers
Summary
Analyses of multicenter studies often need to account for center clustering to ensure valid inference. Authors of a recent review of multicenter studies published in four major medical journals (BMJ, New England Journal of Medicine, JAMA, and The Lancet) found that only 22% of randomized controlled trials (RCTs) with a binary outcome reported accounting for a center effect, a rate similar to past reviews [5, 6]. This result may be due to the fact that it is challenging to properly adjust for center when there are few centers, total sample size is small, or there are few events per center. Clear practical guidelines for the statistical analyses and reporting of multicenter studies are needed to assist investigators and data analysts in conducting appropriate multicenter analyses.
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