Sequential Designs for Individualized Dosing in Phase I Cancer Clinical Trials

This dissertation presents novel sequential dose-finding designs that adjust for inter-individual pharmacokinetic variability in phase I cancer clinical trials. Unlike most traditional dose-finding designs whose primary goals are the determination of a maximum safe dose, the goal of our proposed designs is to estimate a patient-specific dosing function such that the responses of patients can achieve a target safety level. Extending from a single compartment model in the pharmacokinetic theory, we first postulate a linear model to describe the relationship between the area under concentration-time curve, dose and predicted clearance. We propose a repeated least squares procedure that aims to sequentially determine dose according to individual ability of metabolizing the drug. To guarantee consistent estimation of the individualized dosing function at the end of a trial, we apply repeated least squares subject to a consistency constraint based on an eigenvalue theory for stochastic linear regression. We empirically determine the convergence rate of the eigenvalue constraint using a real data set from an irinotecan study in colorectal carcinoma patients, and calibrate the procedure to minimize a loss function that accounts for the dosing costs of study subjects and future patients. When compared to the traditional body surface area and an equation based dosing methods, the simulation results demonstrate that the repeated least squares procedure control the dosing cost and allow for precise estimation of the dosing function. Furthermore, in order to enhance the generality and robustness of the dose-finding designs, we generalize the linear association to a nonlinear relationship between the response and a linear combination of dose and predicted clearance. We propose a two-stage sequential design, the semiparametric link-adapted recursion, which targets at individualizing dose assignments meanwhile adapting for an unknown nonlinear link function connecting the response and dose along with predicted clearance. The repeat least squares with eigenvalue constraint design is utilized as the first stage, and the second stage recursively applies an iterative semiparametric least squares approach to estimate the dosing function and determine dosage for next patient. The simulation results demonstrate that: at first, the performance of repeated least squares with eigenvalue constraint design is acceptably robust to model misspecifications; at second, as its performance is close to that of repeated least squares procedure under parametric models, the semiparametric link-adapted recursion does not sacrifice much estimation accuracy to gain robustness against model misspecifications; at last, compared to the repeated least squares procedure, the semiparametric link-adapted recursion can significantly improve the dosing costs and estimation precision under the semiparametric models.