Unified Approaches for Frequentist and Bayesian Methods in Two-Sample Clinical Trials with Binary Endpoints

Two opposing paradigms, analyses via frequentist or Bayesian methods, dominate the statistical literature. Most commonly, frequentist approaches have been used to design and analyze clinical trials, though Bayesian techniques are becoming increasingly popular. However, these two paradigms can generate divergent results even in analyses of the same trial data, which may harm the scientific interpretability of the trial. Therefore, it is crucial to harmonize analyses under each approach. In this dissertation, novel unified approaches for one-sided frequentist and Bayesian hypothesis testing problems comparing two proportions in fixed-sample and group-sequential clinical trials are proposed. When a frequentist design with desired type I and II error rates are given, the unification is achieved by deriving specific Bayesian decision thresholds and sample sizes. Similarly, when a Bayesian design is given, the unification is achieved by deriving corresponding frequentist characteristics. In addition, theoretical methods to determine the Bayesian decision threshold, sample size and power are provided. Numerical results show that the unified approach can yield the same type I and II error rates for frequentist and Bayesian hypothesis tests through a numerical study. Further, detailed evaluations suggest that Bayesian priors specifications, allocation ratios, number of analyses can affect the resulting Bayesian sample sizes and decision thresholds. Overall, the unified approach can be adopted into the current clinical trial setting and is helpful to make trial results translatable between frequentist and Bayesian methods

A Bayesian Sample Size Estimation Procedure Based on a B-Splines Semiparametric Elicitation Method

Sample size estimation is a fundamental element of a clinical trial, and a binomial experiment is the most common situation faced in clinical trial design. A Bayesian method to determine sample size is an alternative solution to a frequentist design, especially for studies conducted on small sample sizes. The Bayesian approach uses the available knowledge, which is translated into a prior distribution, instead of a point estimate, to perform the final inference. This procedure takes the uncertainty in data prediction entirely into account. When objective data, historical information, and literature data are not available, it may be indispensable to use expert opinion to derive the prior distribution by performing an elicitation process. Expert elicitation is the process of translating expert opinion into a prior probability distribution. We investigated the estimation of a binomial sample size providing a generalized version of the average length, coverage criteria, and worst outcome criterion. The original method was proposed by Joseph and is defined in a parametric framework based on a Beta-Binomial model. We propose a more flexible approach for binary data sample size estimation in this theoretical setting by considering parametric approaches (Beta priors) and semiparametric priors based on B-splines

A Likelihood-Based Approach to Early Stopping in Single Arm Phase II Clinical Trials

Phase II studies in oncology have evolved over the previous several decades. Currently, the number of drugs in phase II development has increased, and patient eligibility has narrowed due to targeted agents, competing trials and curative therapies in the first-line setting. As a result of these changes, more attention needs to be focused toward conducting more efficient phase II trials. Given the increased difficulty in accruing patients to phase II studies and the ethical concern of treating patients with agents that are ineffective, there is significant motivation to stop a single arm trial early when the investigational agent shows evidence of a low response rate