Ph. D. APPLIED STATISTICS DISSERTATION DEFENSE

Model-based clinical trial designs have drawn much attention from the biostatistical community since 1990 when O’Quigley et al. proposed the Continual Reassessment Method (CRM). CRM and its various modified versions have achieved great successes in finding the maximum tolerated dose (MTD) adaptively in the case of dichotomous toxicity responses (i.e. dose-limiting toxicity, DLT, or non-DLT). In dose-escalation processes, it is crucial to differentiate severity of DLT if the impact of severity of toxicity is substantial (e.g. liver toxicities). However, due to the limitation of its model structure, it is difficult to extend CRM naturally to the polychotomous toxicity responses. In this research, we propose a two-parameter probit model with latent variables to extend the CRM for the cases of dichotomous and polychotomouse toxicity responses. For the dichotomous toxicity responses, simulation results under different scenarios show that the proposed model is superior to the power model originally used in the CRM. We extend the proposed model naturally to the ploychotomous toxicity responses by categorizing the latent variables corresponding to the bin boundary parameters. Simulation results show that two-parameter probit model with latent variables works encouragingly well in the case of polychotomous toxicity responses. By differentiating severity of DLT, the number of patients allocated to the higher toxicity dose level is reduced. That reduces the risk of toxicity for patients in the clinical trial study. In addition, we introduce the concept of the overall MTD which makes it possible to study both dichotomous and polychotomous response models under a unified framework. Analytic properties of the overall MTD are given. It is shown that dichotomous response model is a special case of polychotomous response model and under certain circumstances the polychotomous response model is reduced to dichotomous responses model. Furthermore, we generalize the concept of the overall MTD to a broader case. Under this concept, a unified model is built, which includes categorical (such as dichotomous and polychotomous) and numerical (such as continuous) toxicity responses as its special cases. The Convergence, Robustness and Reduction theorems of the overall MTD are proved in the general case. As an example of the continuous toxicity response, the normal toxicity response is studied along with a family of the target toxicity probabilities. Supervising Professor: Keying Ye, Ph.D. Open to all Faculty and Students