Statistical Methods for Bayesian Clinical Trial Design and DNA Methylation Deconvolution

We consider the Bayesian clinical trial design problem in situations where a historical trial is available to inform the design and analysis of a future trial. Currently the FDA requires that all proposed designs exhibit reasonable type I error control. Traditionally, frequentist type I error control has been required. This is currently the case in the Center for Drug Evaluation and Research but no longer in the Center for Devices and Radiological Health. The requirement that a design exhibit frequentist type I error control necessitates that all prior information be discarded. We propose several Bayesian solutions that balance the need to control type I errors with the desire to utilize high quality prior information. For scenarios where the historical trial informs the parameter being tested, we propose Bayesian versions of the type I error rate and power that are defined with respect to the posterior distribution for the parameters given the historical data and conditional on the respective hypothesis being true. We demonstrate that in designs that control the Bayesian type I error rate, meaningful amounts of prior information can be borrowed but that the size of the new trial must be relatively large to justify borrowing a large amount of historical information. We tailor our design methodology for survival applications using proportional hazards and cure rate models. We also develop Bayesian adaptive designs for large cardiovascular outcomes trials (CVOTs) which incorporate control information from a historical CVOT conducted in a similar patient population. We propose an all-or-nothing adaptive design utilizing the power prior as well as a dynamic borrowing adaptive design utilizing a novel extension of the joint power prior. Separately, we present a statistical deconvolution method for DNA methylation data from bisulfite sequencing experiments. We propose a joint model for methylation data from a set of heterogeneous tissue samples and another set of reference tissue samples. Unlike other methylation deconvolution methods, our method allows one to estimate the heterogeneous tissue composition and provides improved estimates of cell type-specific methylation levels through the process of deconvolution. We demonstrate our method using data from DNA mixture tissues and simulation studies.Doctor of Philosoph