Including random centre effects in design, analysis and presentation of multi-centre trials

Background In large multicentre trials in diverse settings, there is uncertainty about the need to adjust for centre variation in design and analysis. A key distinction is the difference between variation in outcome (independent of treatment) and variation in treatment effect. Through re-analysis of the CRASH-2 trial (2010), this study clarifies when and how to use multi-level models for multicentre studies with binary outcomes. Methods CRASH-2 randomised 20,127 trauma patients across 271 centres and 40 countries to either single-dose tranexamic acid or identical placebo, with all-cause death at 4 weeks the primary outcome. The trial data had a hierarchical structure, with patients nested in hospitals which in turn are nested within countries. Reanalysis of CRASH-2 trial data assessed treatment effect and both patient and centre level baseline covariates as fixed effects in logistic regression models. Random effects were included to assess where there was variation between countries, and between centres within countries, both in underlying risk of death and in treatment effect. Results In CRASH-2, there was significant variation between countries and between centres in death at 4 weeks, but absolutely no differences between countries or centres in the effect of treatment. Average treatment effect was not altered after accounting for centre and country variation in this study. Conclusions It is important to distinguish between underlying variation in outcomes and variation in treatment effects; the former is common but the latter is not. Stratifying randomisation by centre overcomes many statistical problems and including random intercepts in analysis may increase power and decrease bias in mean and standard error estimates.