Adaptive design towards optimal dose

Abstract

Adaptive designs have been proposed for ethical concerns, their characteristics, especially in statistics, are widely investigated in the literature. In this thesis, we investigate adaptive designs which direct the trials to an optimal dose level by using Generalized Friedman's Urn Model (GFU), considering the patients' covariates on the probability of success for each dose. A generalized linear model(GLM) is employed with consideration of the patients' covariates and the dose levels simultaneously. The limiting properties of the Maximum Likelihood Estimation(MLE), especially its Central Limit Theorem (CLT) are established in the circumstance that the response variables are dependent. The asymptotic properties of Urn composition and allocation proportion are investigated. Simulations are conducted to verify these properties.