Term of Award

Summer 2018

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Arpita Chatterjee

Committee Member 1

Stephen Carden

Committee Member 2

Divine Wanduku


Non inferiority clinical trials have gained immense popularity within the last decades. Such trials are designed to demonstrate that a new experimental drug is not unacceptably worse than an active control by more than a pre-specified margin. The experimental treatment may not be as good as the active control concerning efficacy, however, the former may offer substantial benefits over the later such as less invasive, lower toxicity, cost-effective, etc. Therefore, a slightly less efficacious treatment can still be acceptable as a treatment alternative to certain groups of patients. Three-arm non-inferiority trials, involving an active control along with an experimental treatment and a placebo arm, have been widely acknowledged as the Gold Standard because they can simultaneously establish both non-inferiority and the assay sensitivity of the treatment under same study. Bayesian approach to assess non-inferiority under continuous end-point has been studied in recent past but such models were never investigated using count data. One obvious recommendation will be the choice of Poisson distribution to model the primary end-point, but Poisson distribution is often affected by over-dispersion. Instead, a Poisson and Gamma mixture, which ultimately results in \textit{Negative Binomial Distribution}, can be a suitable alternative to model count data. In this paper, we propose a Bayesian hierarchical model to perform simultaneous testing of non-inferiority and assay sensitivity in a three-arm trial under the situation that the primary endpoints are negative binomially distributed in the presence of placebo-controlled historical trial. The Bayesian approach allows for the inclusion of historical information by constructing appropriate prior to the current trials, which may result in a significant reduction of sample size while preserving high power. Furthermore, we examined the effect of power prior (Ibrahim and Chen, 2000) under the proposed model setup through a simulation study. Finally, the performance of the proposed model is evaluated based on simulated dataset under varying scenarios

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