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Developing practical guidance for design and analysis of cluster randomised trials to match the chosen estimand

   Faculty of Population Health Sciences

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  Dr A Copas  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Cluster randomised trials involve randomising groups of participants (e.g. hospitals, schools, villages) to different interventions. Participants in the same cluster are typically correlated (more similar to each other than to participants in other clusters), which needs to be accounted for during analysis, otherwise standard errors, confidence intervals, and p-values will be incorrect. Standard methods of analysis are mixed-effects models and GEEs with exchangeable correlation structures, however recent work has shown ( these estimators are biased when the cluster-size is informative (i.e. cluster sizes vary and outcomes or treatment effects differ between larger and smaller clusters). Informative cluster size can occur for a number of reasons, such as differences in quality or experience of staff or differences in types of participants presenting between smaller and larger clusters. Independence estimating equations (IEEs) pose an unbiased alternative, and can be simply weighted according to whether our chosen estimand is the participant-average or cluster-average treatment effect. A cluster summary analysis can sometimes alternatively be used. However these methods have not been well-studied in the context of cluster randomised trials and practical guidance is urgently needed.

This studentship will encompass a number of work packages to address how cluster randomised trials should be designed and analysed in order to provide estimates of treatment effect which are unbiased for the chosen estimand, efficient, and have good statistical properties (e.g. correct type I error rate/confidence intervals). These work packages will include:

·      Evaluating the bias and relative efficiency of mixed-effects models/GEEs with exchangeable correlation structures compared to IEE according to how strongly cluster size is informative, how variable is the cluster size, and other trial features

·      Based on this evaluation develop guidance on the ‘trade-offs’ between methods and consider when, if ever, mixed-effects models/GEEs can be recommended, given their risk of bias

·      Evaluate the performance of different small sample corrections for IEEs when the number of clusters is small, to identify which methods are appropriate to use in small sample settings 

·      Derive sample size formulas for IEEs, both when informative cluster size is and is not anticipated

·      Developing guidance on choice of estimand and implications if trial participants are samples from larger clusters 

·      Re-analyse a series of completed cluster randomised trials using the different methods studied above to compare how methods perform in practice

·      Extend the methods derived above to other clustered settings, such as cluster-crossover trials and stepped-wedge trials, time-permitting

The studentship will also involve attendance at a number of training courses (e.g. for simulation studies, cluster randomised trials, etc) as well as conferences and workshops.

Professor Copas and Dr Kahan are both published experts in cluster randomised trials, and will meet regularly with the student to discuss progress, and help identify solutions to any problems. An advisory board will also serve as a wider thesis committee.

The host department (MRC CTU at UCL) is committed to PPI in its clinical research, and is currently developing ways to ensure active PPI across its methodological research, having set up a Methodology PPI panel. The successful student and their supervisors will make use of the panel and existing institutional support to develop a PPI plan for the project.


You are applying for a PhD studentship from the MRC TMRP DTP. A list of potential projects and the application form is available online at:

Please complete the form fully. Incomplete forms will not be considered. CVs will not be accepted for this scheme.

Please apply giving details for your first choice project. You can provide details of up to two other TMRP DTP projects you may be interested in at section B of the application form.

Before making an application, applicants should contact the project supervisor to find out more about the project and to discuss their interests in the research before 09 January 2023.

The deadline for applications is 4pm (GMT) 16 January 2023. Late applications will not be considered.

Completed application forms must be returned to: [Email Address Removed]

Informal enquiries may be made to Professor Copas - [Email Address Removed]

Funding Notes

Studentships are funded by the Medical Research Council (MRC) for 3 years. Funding will cover tuition fees at the UK rate only, a Research Training and Support Grant (RTSG) and stipend. We aim to support the most outstanding applicants from outside the UK and are able to offer a limited number of bursaries that will enable full studentships to be awarded to international applicants. These full studentships will only be awarded to exceptional quality candidates, due to the competitive nature of this scheme.

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