Physical Sciences and Mathematics Commons^™

Creating Regression Model For Non-Markov Transition Probability Using Pseudo-Observations, Michael Gray

Dissertations and Theses

A multi-state model is a graphical tool widely used to illustrate a transitional relationship between states in many applications. We will study the transition probabilities of an illness-death model, which is an example of a multi-state model. We will investigate transition probabilities using a counting process approach. Aalen-Johansen estimator is the gold-standard in estimating a transition probability. However, Aalen-Johansen estimator may be biased when the Markov assumption is violated. Therefore, Aalen-Johansen estimator is an unreliable estimator when the Markov assumption is violated. Several papers have published non-parametric estimators that accommodate for non-Markov models using a counting process approach.

Furthermore, there …

Identifying Advantages To Teaching Linear Regression In A Modeling And Simulation Introductory Statistics Curriculum, Kit Harris Clement

Dissertations and Theses

Statistical association is a key facet of statistical literacy: claims based on relationships between variables or ideas rooted in data are found everywhere in media and discourse. A key development in introductory statistics curricula is the use of simulation-based inference, which has shown positive outcomes for students, especially in regards to statistical literacy and conceptual understanding. In this dissertation project, I investigate students from the Change Agents for the Teaching and Learning of STatistics (CATALST) curriculum in activities I designed for learning statistical association and linear regression. First, I analyzed the informal line fitting strategies of CATALST students. Findings suggest …

A Bayesian Latent Scale Model For Multivariate Longitudinal Data, Kruti Pandya

Dissertations and Theses

In order to understand the entire course of slow progressing diseases like Alzheimer's dementia or multiple sclerosis, it is essential to characterize long term disease dynamics from a healthy stage to a late disease stage. Cohort studies typically recruit subjects at different stages of the disease and then follow them for a relatively short period of time. In this dissertation, we propose a novel Bayesian nonlinear mixed effects model with latent time scale to characterize long term disease dynamics using the observed short term longitudinal data from cohort studies without relying on clinical diagnosis. This model can accommodate noisy longitudinal …

Statistical Analysis Of Social Network Change, Teresa Danielle Schmidt

Dissertations and Theses

This project explores two statistical methods that infer social network structures and statistically test those structures for change over time: regression-based differential network analysis (R-DNA) and information theory-based differential analysis (I-DNA). R-DNA is adapted from bioinformatics and I-DNA employs reconstructability analysis.

This project applies both R-DNA and I-DNA to analyze Medicaid claims data from one-year periods before (May 2011- Apr 2012) and after (Jan 2013-Dec 2013) the formation of the Health Share of Oregon Coordinated Care Organization (CCO). The formation of CCOs was legislated by the state of Oregon in 2012 with the triple aim of improving health outcomes, reducing …

Estimation Of Association Between A Longitudinal Marker And Interval-Censored Progression Times, Naghmeh Daneshi

Dissertations and Theses

In longitudinal studies, we observe the subjects who are likely to progress to a new state during the study time. For example, in clinical trials the stage of a progressing disease is recorded at each follow-up visit. The primary goal is to estimate the relationship between the attributes and the subject's progression state. In such studies, some subjects complete all their follow-up visits and their progression state are observed without any missingness. However, others miss their follow-up visits and when they come back, they learn that they have progressed to a new state. In this case, not only are their …

Investigating Statistics Teachers' Knowledge Of Probability In The Context Of Hypothesis Testing, Jason Mark Asis Dolor

Dissertations and Theses

In the last three decades, there has been a significant growth in the number of undergraduate students taking introductory statistics. As a result, there is a need by universities and community colleges to find well-qualified instructors and graduate teaching assistants to teach the growing number of statistics courses. Unfortunately, research has shown that even teachers of introductory statistics struggle with concepts they are employed to teach. The data presented in this research sheds light on the statistical knowledge of graduate teaching assistants (GTAs) and community college instructors (CCIs) in the realm of probability by analyzing their work on surveys and …

Global Resource Management Of Response Surface Methodology, Michael Chad Miller

Dissertations and Theses

Statistical research can be more difficult to plan than other kinds of projects, since the research must adapt as knowledge is gained. This dissertation establishes a formal language and methodology for designing experimental research strategies with limited resources. It is a mathematically rigorous extension of a sequential and adaptive form of statistical research called response surface methodology. It uses sponsor-given information, conditions, and resource constraints to decompose an overall project into individual stages. At each stage, a "parent" decision-maker determines what design of experimentation to do for its stage of research, and adapts to the feedback from that research's potential …

Application Of Inter-Die Rank Statistics In Defect Detection, Vivek Bakshi

Dissertations and Theses

This thesis presents a statistical method to identify the test escapes. Test often acquires parametric measurements as a function of logical state of a chip. The usual method of classifying chips as pass or fail is to compare each state measurement to a test limit. Subtle manufacturing defects are escaping the test limits due to process variations in deep sub-micron technologies which results in mixing of healthy and faulty parametric test measurements. This thesis identifies the chips with subtle defects by using rank order of the parametric measurements. A hypothesis is developed that a defect is likely to disturb the …

Finite Sample Properties Of Minimum Kolmogorov-Smirnov Estimator And Maximum Likelihood Estimator For Right-Censored Data, Jerzy Wieczorek

Dissertations and Theses

MKSFitter computes minimum Kolmogorov-Smirnov estimators (MKSEs) for several different continuous univariate distributions, using an evolutionary optimization algorithm, and recommends the distribution and parameter estimates that best minimize the Kolmogorov-Smirnov (K-S) test statistic. We modify this tool by extending it to use the Kaplan-Meier estimate of the cumulative distribution function (CDF) for right-censored data. Using simulated data from the most commonly-used survival distributions, we demonstrate the tool's inability to consistently select the correct distribution type with right-censored data, even for large sample sizes and low censoring rates. We also compare this tool's estimates with the right-censored maximum likelihood estimator (MLE). While …

Fundamental Conditions For The Evolution Of Altruism: Towards A Unification Of Theories, Jeffrey Alan Fletcher

Dissertations and Theses

In evolutionary theory the existence of self-sacrificing cooperative traits poses a problem that has engendered decades of debate. The principal theories of the evolution of altruism are inclusive fitness, reciprocal altruism, and multilevel selection. To provide a framework for the unification o f these apparently disparate theories, this dissertation identifies two fundamental conditions required for the evolution of altruism: 1) non-zero-sum fitness benefits for cooperation and 2) positive assortment among altruistic behaviors. I demonstrate the underlying similarities in these three theories in the following two ways. First, I show that the game-theoretic model of the prisoner’s dilemm a (PD) is …

Probability Driven Heuristic Nets, Lynn Robert Carter

Dissertations and Theses

Let a probability driven switch be defined as a switch of three input paths and three output paths. The status of the input paths defines a probability for each output path (as to whether it will generate a signal or not.) One output path is linked to one input path, so the results of the switch at time t can affect the switch at time t+1. A switch so constructed can be defined (by the probabilities) to take on the function of the standard logic gates (AND, OR, …) A net constructed of these switches can be “taught” by …

A Review Of "Longitudinal Study" In Developmental Psychology, Emily H. Finley

Dissertations and Theses

The purpose of this library research thesis is to review the "longitudinal study" in terms of problems and present use. A preliminary search of the literature on longitudinal method revealed problems centering around two areas: (1) definition of "longitudinal study" and (2) practical problems of method itself. The purpose of this thesis then is to explore through a search of books and journals the following questions:

1. How can “longitudinal study” be defined?

2. What problems are inherent in the study of the same individuals over time and how can these problems be solved?

A third question which emerges from …