An Optimization Approach for the Parameter Estimation of the Nonlinear Mixed Effects Models

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Title: An Optimization Approach for the Parameter Estimation of the Nonlinear Mixed Effects Models
Author: Wang, Jing
Advisors: Bhattacharyya, Bibhuti, Committee Member
John F. Monahan, Committee Chair
Marie Davidian, Committee Member
Dickey, David, Committee Member
Abstract: Nonlinear mixed-effects models (NLMM) have received a great deal of attention in the statistical literature in recent years because of the flexibility they offer in handling the unbalanced repeated-measurements data that arise in different areas of investigation, such as pharmacokinetics. We concentrate here on maximum likelihood estimation for the parameters in nonlinear mixed-effects models. A rather complex numerical issue for maximum likelihood estimation in nonlinear mixed-effects models is the evaluation of a multiple integral that, in most cases, does not have a closed-form expression. We restrict our attention in this article on numerical methods that are based on approximation for the likelihood. Several numerical approximations for the likelihood have been proposed such as first-order linearization (FOL), Laplace approximation, Importance Sampling, and Gaussian Quadrature (GQ). In addition, for a general optimization problem, iterative methods are usually required to update the parameter estimates iteratively. A large number of parameter updating methods have been developed such as Newton-Raphson, Steepest Descent, Stochastic optimization, etc. Many current optimization algorithms implement a Newton iterative method to update the parameter estimates in NLMM. The objective of this thesis is to propose an optimization approach for the parameter estimation in nonlinear mixed-effects models. This optimization method implements Importance Sampling for approximating likelihood and a stochastic recursive procedure for updating parameter estimates in NLMM. In Chapter 1, we describe the model and introduce several likelihood approximations and parameter updating procedures for these models. The proposed optimization approach is illustrated in Chapter 2. In order to compare this approach to the other optimization methods, simulations are performed and conclusions are drawn based on simulation results in Chapter 3. Some future work is presented in Chapter 4.
Date: 2004-07-29
Degree: PhD
Discipline: Statistics

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