Organizational Unit:
H. Milton Stewart School of Industrial and Systems Engineering
H. Milton Stewart School of Industrial and Systems Engineering
Permanent Link
Research Organization Registry ID
Description
Previous Names
Parent Organization
Parent Organization
Organizational Unit
Includes Organization(s)
Organizational Unit
ArchiveSpace Name Record
Publication Search Results
Now showing
1 - 3 of 3
-
ItemComputational advances for big data analytics and medical decision making(Georgia Institute of Technology, 2020-08-27) Li, ZhuonanWith the increase in volume and complexity of data and evidence, medical decision making can be a complex process. Many decisions involve timeliness, uncertainties, and tradeoffs, and can have serious consequences for patients and the clinical practice. This dissertation aims to develop computationally efficient methods for big data analytics and medical decision making. We investigate three topics: the double pivot simplex method to advance linear programming solution techniques, the multiple isocenter selection problem in radiation therapy treatment planning, and the multi-objective treatment planning optimization problem. Chapter 1 advances the computation aspects of the double pivot simplex method by improving its computational efficiency and stability. The double pivot simplex method is a recent advancement to the simplex method which optimally solves linear programs. During any iteration, this algorithm pivots up to two variables at a time instead of one. An efficient implementation of double pivots is developed into LPSOL, a simplex solver for linear programs. We discuss a procedure to handle double pivots and bounded variables, a strategy to update the basis factorization with two variables simultaneously, and other topics related to numerical instability. On average, this implementation enabled double pivots to solve benchmark problems with nearly 30% fewer pivots and in better than 25% less time than the classical single pivots. In Chapter 2, we study the multiple isocenters placement problem in external beam radiation therapy treatment planning. In current treatment strategies, most plans use a single isocenter. Multiple isocenters can improve the dose conformity but their number and locations are difficult to determine. To address this issue, we propose a mathematical model which incorporates the tumor’s geometric characteristics to determine the number of isocenters. An approximation heuristic approach is developed to solve the isocenter selection problem. With the optimized isocenters, the treatment plans can achieve better conformity compared to single isocenter plans. In Chapter 3, we propose a radiation therapy treatment planning framework for stereotactic body radiation treatment (SBRT). Beam angles and the final aperture shapes are critical in developing feasible and deliverable radiation treatment plans. Here we propose the first treatment planning framework that combines the two by integrating the warm-start simultaneous beam angle and fluence map optimization (BAFMO) and direct aperture optimization (DAO). Both problems are multiple objective optimization problems. We introduce the matrix reduction technique to handle dense dose matrix for BAFMO and an approximation scheme for column generation in DAO. We further investigate the benefit of utilizing the optimized beam angle from the BAFMO and show that the final plans use 20% less total modular units (MU) of typical radiation doses.
-
ItemSequential interval estimation for Bernoulli trials(Georgia Institute of Technology, 2018-07-31) Yaacoub, TonyInterval estimation of a binomial proportion is one of the most-basic problems in statistics with many important real-world applications. Some classical applications include estimation of the prevalence of a rare disease and accuracy assessment in remote sensing. In these applications, the sample size is fixed beforehand, and a confidence interval for the proportion is obtained. However, in many modern applications, sampling is especially costly and time consuming, e.g., estimating the customer click-through probability in online marketing campaigns and estimating the probability that a stochastic system satisfies a specific property as in Statistical Model Checking. Because these applications tend to require extensive time and cost, it is advantageous to reduce the sample size while simultaneously assuring satisfactory quality (coverage) levels for the corresponding interval estimates. The sequential version of the interval estimation aims at the latter goal by allowing the sample size to be random and, in particular, formulating a stopping time controlled by the observations themselves. The literature focusing on the sequential setup of the problem is limited compared to its fixed sample-size counterpart, and sampling procedure optimality has not been established in the literature. The work in this thesis aims to extend the body of knowledge on the topic of sequential interval estimation for Bernoulli trials, addressing both the theoretical and practical concerns. In the first part of this thesis, we propose an optimal sequential methodology for obtaining fixed-width confidence intervals for a binomial proportion when prior knowledge of the proportion is available. We assume that there exists a prior distribution for the binomial proportion, and our goal is to minimize the expected number of samples while guaranteeing that the coverage probability is at least a specified nominal coverage probability level. We demonstrate our stopping time is always bounded from above and below; we will need to first accumulate a sufficient amount of information before we start applying our stopping rule, and our stopping time will always terminate in finite time. We also compare our method with the optimum fixed-sample-size procedure as well as with existing alternative sequential schemes. In the second part of this thesis, we propose a two-stage sequential method for obtaining tandem-width confidence intervals for a binomial proportion when no prior knowledge of the proportion is available and when it is desired to have a computationally efficient method. By tandem-width, we mean that the half-width of the confidence interval of the proportion is not fixed beforehand; it is instead required to satisfy two different upper bounds depending on the underlying value of the binomial proportion. To tackle this problem, we propose a simple but useful sequential method for obtaining fixed-width confidence intervals for the binomial proportion based on the minimax estimator of the binomial proportion. Finally, we extend the idea for Bernoulli distributions in the first part of this thesis to interval estimation for arbitrary distributions, with an alternative optimality formulation. Here, we propose a conditional cost alternative formulation to circumvent certain analytical/computational difficulties. Specifically, we assume that an independent and identically distributed process is observed sequentially with its common probability density function having a random parameter that must be estimated. We follow a semi-Bayesian approach where we assign cost to the pair (estimator, true parameter), and our goal is to minimize the average sample size guaranteeing at the same time an average cost below some prescribed level. For a variety of examples, we compare our method with the optimum fixed-sample-size and other existing sequential schemes.
-
ItemEfficient change detection methods for bio and healthcare surveillance(Georgia Institute of Technology, 2010-06-14) Han, Sung WonFor the last several decades, sequential change point problems have been studied in both the theoretical area (sequential analysis) and the application area (industrial SPC). In the conventional application, the baseline process is assumed to be stationary, and the shift pattern is a step function that is sustained after the shift. However, in biosurveillance, the underlying assumptions of problems are more complicated. This thesis investigates several issues in biosurveillance such as non-homogeneous populations, spatiotemporal surveillance methods, and correlated structures in regional data. The first part of the thesis discusses popular surveillance methods in sequential change point problems and off-line problems based on count data. For sequential change point problems, the CUSUM and the EWMA have been used in healthcare and public health surveillance to detect increases in the rates of diseases or symptoms. On the other hand, for off-line problems, scan statistics are widely used. In this chapter, we link the method for off-line problems to those for sequential change point problems. We investigate three methods--the CUSUM, the EWMA, and scan statistics--and compare them by conditional expected delay (CED). The second part of the thesis pertains to the on-line monitoring problem of detecting a change in the mean of Poisson count data with a non-homogeneous population size. The most common detection schemes are based on generalized likelihood ratio statistics, known as an optimal method under Lodern's criteria. We propose alternative detection schemes based on the weighted likelihood ratios and the adaptive threshold method, which perform better than generalized likelihood ratio statistics in an increasing population. The properties of these three detection schemes are investigated by both a theoretical approach and numerical simulation. The third part of the thesis investigates spatiotemporal surveillance based on likelihood ratios. This chapter proposes a general framework for spatiotemporal surveillance based on likelihood ratio statistics over time windows. We show that the CUSUM and other popular likelihood ratio statistics are the special cases under such a general framework. We compare the efficiency of these surveillance methods in spatiotemporal cases for detecting clusters of incidence using both Monte Carlo simulations and a real example. The fourth part proposes multivariate surveillance methods based on likelihood ratio tests in the presence of spatial correlations. By taking advantage of spatial correlations, the proposed methods can perform better than existing surveillance methods by providing the faster and more accurate detection. We illustrate the application of these methods with a breast cancer case in New Hampshire when observations are spatially correlated.