Subjective Bayesian Methods in the Design and Analysis of Clinical Trials

Abstract

Assurance provides a Bayesian alternative to commonly used frequentist sample size calculation methods. As part of sample size calculations, an estimate of a treatment’s effect size or a test’s accuracy is typically required. When using Bayesian methods, these unknown quantities can be represented with a prior distribution, rather than using a single point estimate, allowing for more nuanced information about the unknown quantity to be incorporated into the sample size calculation. In this thesis, we first review common sample size calculation methods and elicitation techniques. We consider the problem of aggregating expert prior beliefs to form a single prior distribution, to be used in sample size calculations. Common methods of prior distribution aggregation include mathematical methods, which use a mathematical rule to combine priors, and behavioural methods, which provide experts with a framework to assist them in creating an aggregate prior during a group discussion. Though not a recent development, assurance is not commonly used in practice. We provide a case study of a diagnostic study, investigating a novel diagnostic test for Motor Neurone Disease, for which prior distributions are elicited and aggregated across experts, and sample size calculations are conducted using both frequentist and assurance methods. As a result of the requirements involved in using each method of aggregation, few comparisons between behavioural and mathematical aggregation methods exist. In order to make comparisons, we structured a series of elicitations as part of the case study. We demonstrate how any method of aggregation outperforms individual experts, and that the Sheffield Elicitation Framework and Classical Method perform best out of the aggregation methods compared. We also demonstrate that all of the considered aggregation methods perform better than a randomly selected individual expert. In order to explore the behaviour of assurance, we provide a number of simulation studies comparing assurance and power calculations. We investigate the sensitivity of power and assurance to changes in input parameters, the effect of misrepresenting an effect size, and the effect of using different prior distributions in the design and analysis stages of assurance calculations. We consider these behaviours for both Normal and binomial observations. We use the resulting aggregated prior distributions for assurance and power calculations, to determine appropriate sample sizes within the case study and more generally. We compare assurance calculations with different priors, analysis methods and target values to further demonstrate differences between assurance and power, and their properties. We demonstrate how the choice of model and prior distribution can have a large impact on the final results of a sample size calculation.