Optimal Designs for Two-Arm Randomized Phase II Clinical Trials with Multiple Constraints

Abstract

Properly planned and executed clinical trials play a vital role for modern medicine. They have been considered as the most important studies for the development of novel treatments. In particular, designs for phase II clinical trials are crucial for new treatments development and assessment since they determine whether further definitive phase III trials are necessary. Numerous phase II designs have been developed in the last several decades. In practice, however, investigators usually need to spend time to create their own statistical algorithms since only a few conventional approaches were integrated into currently available statistical software. Therefore, developing ready-to-use packages or tools for phase II designs can accelerate, facilitate, and improve the process of designing phase II studies. Moreover, most existing phase II designs were developed in the context of sequential procedures where the main outcome is a response rate. Such designs may be inefficient when endpoints are not binary and cannot be observed within a short period. Furthermore, it has been claimed by many studies that phase II designs with a concurrent control have advantages of better patient comparability and less bias. In this dissertation, we focus on the non-sequential designs for two-arm randomized phase II clinical trials. Specifically, the first paper develops an R package for optimal designs proposed by Mayo et al. (2010) where the total sample sizes are optimized under pre-specified constraints on the standard errors of estimated efficacy rates in both control and experimental arms and the difference between the two rates. However, the designs developed in Mayo et al. (2010) are limited to dichotomous outcomes only. The second paper generalizes the original methods to designs suitable for two-arm randomized phase II trials with endpoints from the exponential dispersion family. The new designs are generalized from a frequentist perspective and the total sample sizes are minimized using multiple constraints optimization based on standard errors. This extension is more broadly applicable to other types of study measures which include several classical distributions such as the normal, exponential, and gamma as special cases. Recently, the Bayesian analysis has become a popular and widely accepted approach to statistics due to its flexibility and ability of incorporating exiting information. The third paper further generalizes the two frequentist designs to the entire exponential family from a Bayesian perspective where the total sample sizes are optimized under constraints on the average length of posterior credible intervals of the group means and the difference between the group means.