Accounting for centre-effects in multicentre trials with a binary outcome - when, why, and how?

It is often desirable to account for centre-effects in the analysis of multicentre randomised trials, however it is unclear which analysis methods are best in trials with a binary outcome. We compared the performance of four methods of analysis (fixed-effects models, random-effects models, generalised estimating equations (GEE), and Mantel-Haenszel) using a re-analysis of a previously reported randomised trial (MIST2) and a large simulation study. The re-analysis of MIST2 found that fixed-effects and Mantel-Haenszel led to many patients being dropped from the analysis due to over-stratification (up to 69% dropped for Mantel-Haenszel, and up to 33% dropped for fixed-effects). Conversely, random-effects and GEE included all patients in the analysis, however GEE did not reach convergence. Estimated treatment effects and p-values were highly variable across different analysis methods.The simulation study found that most methods of analysis performed well with a small number of centres. With a large number of centres, fixed-effects led to biased estimates and inflated type I error rates in many situations, and Mantel-Haenszel lost power compared to other analysis methods in some situations. Conversely, both random-effects and GEE gave nominal type I error rates and good power across all scenarios, and were usually as good as or better than either fixed-effects or Mantel-Haenszel. However, this was only true for GEEs with non-robust standard errors (SEs); using a robust 'sandwich' estimator led to inflated type I error rates across most scenarios. With a small number of centres, we recommend the use of fixed-effects, random-effects, or GEE with non-robust SEs. Random-effects and GEE with non-robust SEs should be used with a moderate or large number of centres.