Hypothesis Testing for Identification and Estimation with Applications to Metamodel Assessment and Adaptive Clinical Trials

Abstract

Within the realm of operations research, hypothesis testing emerges as a crucial instrument for the rigorous assessment of statistical measures, as the reliability of test outcomes heavily relies on the accuracy of these statistical metrics. In this thesis, we provide an in-depth analysis of this statistical methods used to evaluate metamodels and manage patient allocation in adaptive clinical trials. Our research focuses primarily on exploring the asymptotic properties and the applicability of the central limit theorem to these statistics. Such a thorough examination is pivotal in establishing a robust theoretical base, thereby enhancing the precision and trustworthiness of hypothesis testing. This thesis consists of two topics.

Firstly, we undertake the assessment of metamodels for quantile performance. Simulation models serve to illuminate the dynamics of real systems, such as the response of system performance to changes in design parameters. A "metamodel" is essentially a mathematical surrogate designed to replicate the behavior of another model, in our context, it simulates the input-output relationship of quantile performance in simulation models. Evaluating a metamodel's accuracy in approximating an unknown function is crucial before its application. This method helps us overcome the obstacle of directly estimating the true function, while a task often complicated by the "curse of dimensionality". We introduce a novel distance metric specifically for quantile metamodels. Moreover, by applying the central limit theorem and utilizing confidence intervals, we provide statistical validation for our estimator and the hypothesis tests conducted.

Secondly, we develop a framework for patient allocation in adaptive clinical trials using the epsilon-greedy algorithm. Clinical trials are crucial in medical research, designed to evaluate the efficacy and safety of various medical interventions. Our research demonstrates that with our algorithm, over time, the optimal treatment arm is predominantly chosen, aligning with our ethical considerations inherent in clinical trials involving human subjects. These trials require a delicate balance between scientific rigor and the well-being of patients. We have thoroughly examined the asymptotic properties and the central limit theorem's applicability to our statistical methods. These rigorous validations provide a strong theoretical basis for using hypothesis testing in clinical trials.

Date of Award	23 Sept 2024
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Guangwu LIU (Supervisor)