Design and Analysis of Basket Clinical Trials

The rise of precision medicine has ushered in the development of innovative clinical trial designs, notably basket trials, which assess the efficacy of a single therapeutic treatment across multiple disease types simultaneously, with each disease group forming a ‘basket’. Basket trials are advantageous as they allow testing of treatments on rare disease types which do not typically warrant their own investigation due to limited sample sizes. Small sample sizes can result in a lack of statistical power and precision of estimates. Bayesian information borrowing models can be implemented to improve inference by leveraging information from one basket when making inference in another. This thesis develops novel information borrowing methodology to improve power and reduce the type I error rate under various settings. This thesis first explores several existing Bayesian information borrowing models and proposes a novel data-driven adaptation. The models are investigated through simulation studies under numerous settings, including the often-overlooked unequal sample size case. Results indicate that the proposed approach better controls for a type I error, whilst yielding improved power. Approaches for the addition of new baskets to an ongoing trial are also proposed. Our findings demonstrate a substantial improvement in power in new baskets when information borrowing is utilised, though this comes with the risk of error inflation. We propose a novel calibration of efficacy criteria to mitigate this inflation. Simulation results show that implementing this calibration reduces error rates, with only a small loss in power in a few cases. Within the literature there are typically two avenues for information borrowing: borrowing between baskets on a trial or borrowing from historic data. We develop models that amalgamate both forms of borrowing. We show that the incorporation of historic data can improve power of estimates, whilst maintaining similar error rates to a method that ignores historic data.