New Algorithms for D-optimal Designs under General Parametric Models
Creators: name: Huang, Yifei
Publisher: name: University of Illinois at Chicago
Year: 2024

description: In this dissertation, we utilize the optimal design theories to develop two algorithms and provide theoretical justifications for the optimality of our algorithms. The first algorithm is a constrained adaptation of the lift-one algorithm, tailored for sampling in paid research studies. The second algorithm focuses on D-optimal designs for experiments with mixed factors, aiming to reduce distinct experimental settings while maintaining high efficiency.
In Chapter 1, I introduce the fundamental elements of optimal designs, generalized linear models(GLMs), and multinomial linear models(MLMs) along with their respective Fisher in- formation matrices. This chapter also provides a concise overview of the preceding research this dissertation work built upon, such as the optimal designs for multinomial logistic models (1; 2; 3), the optimal design for generalized linear models (4; 5), and lift-one algorithm (6; 7).
In Chapter 2, we consider constrained sampling problems in paid research studies or clinical trials. When there are more qualified volunteers than the budget allowed, we recommend a D- optimal sampling strategy based on the optimal design theory and develop a constrained lift-one algorithm to find the optimal allocation. Unlike the literature, which mainly deals with linear models, our solution solves the constrained sampling problem under fairly general statistical models, including generalized linear models and multinomial logistic models, and with more general constraints. We justify theoretically the optimality of our sampling strategy and show, by simulation studies and real-world examples, the advantages of simple random sampling and proportionally stratified sampling strategies.
In Chapter 3 and Chapter 4, we address the problem of designing an experiment with both discrete and continuous factors under fairly general parametric statistical models. We propose a new algorithm, named ForLion, to search for optimal designs under the D-criterion. The algorithm performs an exhaustive search in a design space with mixed factors while keeping high efficiency and reducing the number of distinct experimental settings. Its optimality is guaranteed by the general equivalence theorem. We demonstrate its superiority over state-of- the-art design algorithms using real-life experiments under multinomial logistic models (MLM) and generalized linear models (GLM). Our simulation studies show that the ForLion algorithm could reduce the number of experimental settings by 25% or improve the relative efficiency of the designs by 17.5% on average. Our algorithm can help the experimenters reduce the time cost, the usage of experimental devices, and thus the total cost of their experiments while preserving high efficiencies of the designs.
I conclude the dissertation work in Chapter 5. Following that, I also propose several prospec- tive directions for future research, building upon the methodologies and results presented herein. Those potential extensions offer future exploration of the framework and applications introduced in this work.