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

Abstract

BackgroundMulticentre 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.MethodsAssuming 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.ResultsWhile 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.ConclusionsAll 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.

Many multicenter trials had few events per center, requiring analysis via random-effects models or GEEs

“…These points are summarized in table 1. More comprehensive descriptions of each method is available elsewhere [1–4, 6, 7]. Additionally, we do not discuss issues such as conditional vs. marginal treatment effects, or treatment by center interactions, both of which have been discussed previously [1–3, 6].…”

“…A large amount of research has compared the different methods of analysis in a variety of settings [1, 2, 4, 6–8]. For continuous outcomes, it is generally agreed that random-effects models will give good results in almost all scenarios [2, 4, 7].…”

“…For continuous outcomes, it is generally agreed that random-effects models will give good results in almost all scenarios [2, 4, 7]. Fixed-effects models can be used provided the number of patients per center is not too small [1, 2].…”

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“…This variability must be accounted for when considering multicentre reproducibility. Mixed-effects modelling provides a statistically robust approach to maximising data inclusion, while acknowledging inevitable slight inconsistencies in the data112.…”

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“…21 The models were constructed using the lmerTest package available on the R software. They were validated by visual inspection of residuals and random slopes distributions on histograms which approximated a normal distribution.…”