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Comparing methods to estimate treatment effects on a continuous outcome in multicentre randomized controlled trials: A simulation study

Rong Chu12*, Lehana Thabane124, Jinhui Ma12, Anne Holbrook134, Eleanor Pullenayegum124 and Philip James Devereaux1

Author Affiliations

1 Department of Clinical Epidemiology and Biostatistics, McMaster University, Health Sciences Centre, Room 2C7, 1200 Main Street West, Hamilton ON, L8N 3Z5, Canada

2 Biostatistics Unit, St Joseph's Healthcare Hamilton, Hamilton ON, Canada

3 Division of Clinical Pharmacology, Department of Medicine, McMaster University, Hamilton ON, Canada

4 Centre for Evaluation of Medicine, St Joseph's Healthcare Hamilton, Hamilton ON, Canada

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BMC Medical Research Methodology 2011, 11:21  doi:10.1186/1471-2288-11-21

Published: 21 February 2011



Multicentre randomized controlled trials (RCTs) routinely use randomization and analysis stratified by centre to control for differences between centres and to improve precision. No consensus has been reached on how to best analyze correlated continuous outcomes in such settings. Our objective was to investigate the properties of commonly used statistical models at various levels of clustering in the context of multicentre RCTs.


Assuming no treatment by centre interaction, we compared six methods (ignoring centre effects, including centres as fixed effects, including centres as random effects, generalized estimating equation (GEE), and fixed- and random-effects centre-level analysis) to analyze continuous outcomes in multicentre RCTs using simulations over a wide spectrum of intraclass correlation (ICC) values, and varying numbers of centres and centre size. The performance of models was evaluated in terms of bias, precision, mean squared error of the point estimator of treatment effect, empirical coverage of the 95% confidence interval, and statistical power of the procedure.


While all methods yielded unbiased estimates of treatment effect, ignoring centres led to inflation of standard error and loss of statistical power when within centre correlation was present. Mixed-effects model was most efficient and attained nominal coverage of 95% and 90% power in almost all scenarios. Fixed-effects model was less precise when the number of centres was large and treatment allocation was subject to chance imbalance within centre. GEE approach underestimated standard error of the treatment effect when the number of centres was small. The two centre-level models led to more variable point estimates and relatively low interval coverage or statistical power depending on whether or not heterogeneity of treatment contrasts was considered in the analysis.


All six models produced unbiased estimates of treatment effect in the context of multicentre trials. Adjusting for centre as a random intercept led to the most efficient treatment effect estimation across all simulations under the normality assumption, when there was no treatment by centre interaction.