Document Type


Date of Award

Spring 5-31-2013

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Sunil Kumar Dhar

Second Advisor

Steven Sun

Third Advisor

Sudhakar Rao

Fourth Advisor

Sundarraman Subramanian

Fifth Advisor

Wenge Guo


In this research, two new designs in clinical trials are proposed. The first problem is a new Bayesian adaptive dose-finding design and its application in an oncology clinical trial. This design is used for phase IB studies with the biomarker as the endpoint and with the fewer patients. The second problem is another new Bayesian adaptive dose-finding design with longitudinal analysis and its application in phase II depression clinical trial. This design is best fit for phase II dosing-finding clinical trials with clinical endpoints. MTD information has been obtained before the trials.

In adaptive dose-finding clinical trials, the strategy is to reduce the allocation of patients to non-informative doses and also save the trial cost. Bayesian adaptive dose finding design has the ability to utilize accumulating data obtained in real time to alter the course of the trial, thereby enabling dynamic allocation to different dosing groups and dropping of ineffective dosing group earlier. In this research, Bayesian adaptive method is used as a new and useful approach that applies to phase IB and phase II dose-finding clinical trials to evaluate safety and efficacy of the study treatment. Response model and Normal Dynamic Linear Models (NDLMs) are applied in stages 1-4. Conditional probability for each parameter in the model is derived using appropriate prior distributions. Markov Chain Monte Carlo (MCMC) method is used to do the simulation. Model parameters with meaningful prior distributions and the posterior quantities are obtained to evaluate the trial results and they help to determine the optimal dose level which can be used in later studies. Simulations are done for different scenarios in the two designs and used to validate the model. Five-thousand simulation trials are conducted to verify the repeatability of the results. The posterior probability of success for the trial is greater than 90% based on the simulation results. The results give clearer idea if one needs to go further to test new dose levels based on the thorough evaluation of the existing partial data. Compared with the other adaptive dose finding strategy, the proposed Bayesian adaptive designs are sensitive and robust to help the investigators draw conclusion as early as possible. The designs can also reduce sample size substantially which in turn leads to savings in cost and time.

Continuous-time Markov model has the advantage over the traditional survival model and can be used to describe disease as a series of probable transitions between health states. This is an attractive feature since it provides the ability to describe the course of disease over time. It can also describe and estimate expected survival in clinical cohort. In this research, continuous-time Markov model is used in the time-to-event analysis in a phase II oncology trial. Six states are defined in the Markov chain which is used in time to progression analysis for 36 patients with neuroendocrine carcinoma. The transition probability matrix P is defined and used to iterate future transition and survival probabilities. The estimate from matrix analysis shows that the results are reliable and comparable with the Kaplan-Meier results.

Included in

Mathematics Commons



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