Cluster Randomised Controlled Trials involve randomising groups of participants, rather than the individual participants themselves, whilst the outcomes are measured on the participants. Whilst there are a number of practical and methodological advantages to such a design, there are also statistical implications, both in terms of study design and sample size calculation, and in analysis. The methodology underpinning the cluster randomised design is now well-established in the statistical literature. However, the overwhelming majority of methodological developments to date have been within the frequentist paradigm, and as such, there is an opportunity to explore methodological developments in the context of Bayesian approaches to the design and analysis of Cluster Randomised Controlled Trials, which is the focus of this thesis. This thesis begins by identifying and quantifying the practical application of Bayesian methods to such cluster randomised trial designs, as well as existing methodological developments in the area, through a methodological systematic review. The review highlights that whilst there have been some efforts to develop Bayesian methodology for Cluster Randomised Controlled Trials, the practical uptake of such methods remains low. Next, a novel application of an informative class of prior distribution, the power prior, is proposed whereby information is borrowed from continuous, clustered, historical data, such as that from a pilot or feasibility study. The performance of this approach is evaluated, and superiority, in comparison to established methods, is demonstrated for certain performance metrics. The novel application of the power prior methodology is then explored in the context of study design and sample size calculation for a Cluster Randomised Controlled Trial, whereby the impact of the use of these new methods is quantified in the context of the impact on type I error and statistical power. It is demonstrated that the adoption of these methods has the potential to reduce sample size requirements, thereby facilitating more efficient trial design and reducing research waste. However, it is also shown that, under the traditional frequentist interpretation, inflated type I error rates can be expected as a result of borrowing information through the power prior. In order to address the limitation of inflated type I error, an approach is presented in which the degree of information borrowing through the power prior is determined in order to control Bayesian type I error at some nominal level. It is shown that by adopting a Bayesian interpretation of design operating characteristics, information borrowing methods can be used whilst maintaining type I error control. Finally, a newly developed R package, PPCRCT is described which allows for straightforward implementation of the methodology presented within this thesis.

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