Statistics and Probability Commons^™

Asymptotic Theory For Three Infinite Dimensional Diffusion Processes, Youzhou Zhou

Open Access Dissertations and Theses

This thesis is centered around three infinite dimensional diffusion processes:

(i). the infinitely-many-neutral-alleles diffusion model [Ethier and Kurtz, 1981],

(ii). the two-parameter infinite dimensional diffusion model [Petrov, 2009] and [Feng and Sun, 2010],

(iii). the infinitely-many-alleles diffusion with symmetric dominance [Ethier and Kurtz, 1998].

The partition structures, the ergodic inequalities and the asymptotic theory of these three models are discussed. In particular, the asymptotic theory turns out to be the major contribution of this thesis.

In Chapter 2, a slightly altered version of Kingman's one-to-one correspondence theorem on partition structures is provided, which in turn becomes a handy tool ...

Likelihood-Based Inferential Methods For Some Flexible Cure Rate Models, Suvra Pal

Open Access Dissertations and Theses

Recently, the Conway-Maxwell Poisson (COM-Poisson) cure rate model has been proposed which includes as special cases some of the well-known cure rate models discussed in the literature. Data obtained from cancer clinical trials are often right censored and the expectation maximization (EM) algorithm can be efficiently used for the determination of the maximum likelihood estimates (MLEs) of the model parameters based on right censored data.

By assuming the lifetime distribution to be exponential, lognormal, Weibull, and gamma, the necessary steps of the EM algorithm are developed for the COM-Poisson cure rate model and some of its special cases. The inferential ...

An Exploration Of “Non-Economic” Damages In Civil Jury Awards, Herbert M. Kritzer, Guangya Liu, Neil Vidmar

Faculty Scholarship

Using three primary data sources plus three supplemental sources discussed in an appendix, this paper examines how well non-economic damages could be predicted by economic damages and at how the ratio of non-economic damages to economic damages changed as the magnitude of the economic damages awarded by juries increased. We found a mixture of consistent and inconsistent patterns across our various datasets. One fairly consistent pattern was the tendency for the ratio of non-economic to economic damages to decline as the amount of economic damages increased. Moreover, the variability of the ratio also tended to decline as the amount of ...

Dr. Stephen Walter: Beyond Disciplinary Boundaries, Avrilynn Ding, Maylynn Ding, Maxwell Tran

The Meducator

Dr. Stephen Walter is a Professor Emeritus in the Department of Clinical Epidemiology and Biostatistics at McMaster University. He is also an Associate Member of the Department of Mathematics and Statistics. Dr. Walter has developed an international reputation for creating and applying statistical methods in biomedical research, particularly for the evaluation of diagnostic tests. His past positions include Chair of the International Clinical Epidemiology Network, Editor of the American Journal of Epidemiology, and Section Editor for the Wiley Encyclopedia of Biostatistics. Most recently, Dr. Walter was inducted as a Fellow into The Royal Society of Canada.

Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation., Ben C. Nolting

Dissertations, Theses, and Student Research Papers in Mathematics

Many organisms, from bacteria to primates, use stochastic movement patterns to find food. These movement patterns, known as search strategies, have recently be- come a focus of ecologists interested in identifying universal properties of optimal foraging behavior. In this dissertation, I describe three contributions to this field. First, I propose a way to extend Charnov's Marginal Value Theorem to the spatially explicit framework of stochastic search strategies. Next, I describe simulations that compare the efficiencies of sensory and memory-based composite search strategies, which involve switching between different behavioral modes. Finally, I explain a new behavioral analysis protocol for identifying ...

Slow Down And Smell The Data, Andrew Laing

Journal of Professional Communication

This review of Nate Silver’s The Signal and the Noise discusses how Silver’s celebrity statistician status has been achieved and is well-earned. He touches on how the book reinforces, in an understandable fashion, that a conceptual understanding of Big Data is a crucial element of successful professional communication practice. This positive review identifies the strengths of Silver’s book – namely its solid organization and its use of real-world examples. The Signal and the Noise is recommended for professional communicators who want to gain an understanding of data and the many uncertainties inherent to its analysis.

©Journal of Professional ...

Statistical Analysis And Modeling Of Prostate Cancer, Yiu Ming Chan

Graduate School Theses and Dissertations

The objective of the present study is to address some important questions related to prostate cancer treatments and survivorship among White and African American men. It is commonly understood that the risk of developing prostate cancer is higher in African American men than the other races. However, using parametric analysis, this study demonstrates that this perception is a "myth" not a "reality". The study further identifies the existence of racial/ethnic disparities by comparing the average mean tumor size, the median of survival time, and the survival function between White and African American men. These results underline the necessity of ...

Polynomially Adjusted Saddlepoint Density Approximations, Susan Zhe Sheng

University of Western Ontario - Electronic Thesis and Dissertation Repository

This thesis aims at obtaining improved bona fide density estimates and approximants by means of adjustments applied to the widely used saddlepoint approximation. Said adjustments are determined by solving systems of equations resulting from a moment-matching argument. A hybrid density approximant that relies on the accuracy of the saddlepoint approximation in the distributional tails is introduced as well. A certain representation of noncentral indefinite quadratic forms leads to an initial approximation whose parameters are evaluated by simultaneously solving four equations involving the cumulants of the target distribution. A saddlepoint approximation to the distribution of quadratic forms is also discussed. By ...

Characterizing Expected Benefits Of Biomarkers In Treatment Selection, Ying Huang, Eric Laber, Holly Janes

UW Biostatistics Working Paper Series

Biomarkers associated with the treatment response heterogeneity hold potential for treatment selection. In practice, the decision regarding whether to adopt a treatment selection marker depends on the effect of treatment selection on the rate of targeted disease as well as additional cost associated with the treatment. We propose an expected benefit measure that incorporates both aspects to quantify a biomarker's treatment selection capacity. This measure extends an existing decision-theoretic framework, to account for the fact that optimal treatment absent marker information varies with the cost of treatment. In addition, we establish upper and lower bounds for the performance of ...

A General Instrumental Variable Framework For Regression Analysis With Outcome Missing Not At Random, Eric J. Tchetgen Tchetgen, Kathleen Wirth

Harvard University Biostatistics Working Paper Series

No abstract provided.

Alternative Identification And Inference For The Effect Of Treatment On The Treated With An Instrumental Variable, Eric J. Tchetgen Tchetgen, Stijn Vansteelandt

Harvard University Biostatistics Working Paper Series

No abstract provided.

Identification And Estimation Of Survivor Average Causal Effects, Eric J. Tchetgen Tchetgen

Harvard University Biostatistics Working Paper Series

No abstract provided.

On The Causal Interpretation Of Race In Regressions Adjusting For Confounding And Mediating Variables, Tyler J. Vanderweele, Whitney Robinson

Harvard University Biostatistics Working Paper Series

We consider different possible interpretations of the “effect of race” when regressions are run with race as an exposure variable, controlling also for various confounding and mediating variables. When adjustment is made for socioeconomic status early in a person's life, we discuss under what contexts the regression coefficients for race can be interpreted as corresponding to the extent to which a racial disparity would remain if various socioeconomic distributions early in life across racial groups could be equalized. When adjustment is also made for adult socioeconomic status, we note how the overall disparity can be decomposed into the portion ...

A Unification Of Mediation And Interaction, Tyler J. Vanderweele

Harvard University Biostatistics Working Paper Series

We show that the overall effect of an exposure on an outcome, in the presence of a mediator with which the exposure may interact, can be decomposed into four components: (i) the effect of the exposure in the absence of the mediator, (ii) the interactive effect when the mediator is left to what is would be in the absence of exposure, (iii) a mediated interaction and (iv) a pure mediated effect. These four components respectively correspond to the portion of the effect that is due to neither mediation nor interaction, to just interaction (but not mediation), to both mediation and ...

Multi-Marker Tests For Joint Association In Longitudinal Studies Using The Genetic Random Field Model, Zihuai He, Min Zhang, Seunggeun Lee, Jennifer A. Smith, Xiuqing Guo, Walter Palmas, Sharon L.R. Kardia, Ana V. Diez Roux, Bhramar Mukherjee

The University of Michigan Department of Biostatistics Working Paper Series

Longitudinal studies of common and chronic diseases risk factors, such as blood pressure, provide a valuable opportunity to explore how genetic variants affect complex traits over time. Statistical power to detect disease susceptibility variants can be improved if we jointly utilize the entire set of longitudinal outcomes. Since disease risk factors and phenotypes are likely influenced by the joint effect of multiple variants in a gene, a joint analysis of these variants considering linkage disequilibrium (LD) and potential interactions among the variants may help to explain additional heritability. In this article, we propose a novel statistical approach: the longitudinal genetic ...

Community College Consortium Promotes Open Educational Practices Through Outreach And Collaboration, Una T. Daly, Lisa Storm, Barbara Illowsky

Open Access Un/Conference

The Community College Consortium for Open Educational Resources (CCCOER) is a community of practice focused on awareness and promoting best practices for OER discovery and adoption including open textbooks, open MOOCs, and open repositories to enhance learning and teaching. Through monthly outreach webinars with OER leaders and online advisory meetings, the community shares their projects and expertise encouraging collaboration across institutions, disciplines, and higher education sectors. Hear from the consortium director and two leaders of the community college OER movement.

• Una Daly, Director of Community College Outreach, OpenCourseWare Consortium. Building a community to promote awareness and shared knowledge of open ...

Hypothesis Testing For An Extended Cox Model With Time-Varying Coefficients, Takumi Saegusa, Chongzhi Di, Ying Qing Chen

UW Biostatistics Working Paper Series

The log-rank test has been widely used to test a treatment effect under the Cox model for censored time-to-event outcomes, though it may lose power substantially when the model's proportional hazards assumption does not hold. In this paper, we consider an extended Cox model that uses B-splines or smoothing splines to model a time-varying treatment effect and propose score test statistics for the treatment effect. Our proposed new tests combine statistical evidence from both the magnitude and the shape of the time-varying hazard ratio function, and thus are omnibus and powerful against various types of alternatives. In addition, the ...

Challenges In Estimating The Causal Effect Of An Intervention With Pre-Post Data (Part 1): Definition & Identification Of The Causal Parameter, Ann M. Weber, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

There is mixed evidence of the effectiveness of interventions operating on a large scale. Although the lack of consistent results is generally attributed to problems of implementation or governance of the program, the failure to find a statistically significant effect (or the success of finding one) may be due to choices made in the evaluation. To demonstrate the potential limitations and pitfalls of the usual analytic methods used for estimating causal effects, we apply the first half of a roadmap for causal inference to a pre-post evaluation of a community-level, national nutrition program. Selection into the program was non-random and ...

Variable Importance And Prediction Methods For Longitudinal Problems With Missing Variables, Ivan Diaz, Alan E. Hubbard, Anna Decker, Mitchell Cohen

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper we present prediction and variable importance (VIM) methods for longitudinal data sets containing both continuous and binary exposures subject to missingness. We demonstrate the use of these methods for prognosis of medical outcomes of severe trauma patients, a field in which current medical practice involves rules of thumb and scoring methods that only use a few variables and ignore the dynamic and high-dimensional nature of trauma recovery. Well-principled prediction and VIM methods can thus provide a tool to make care decisions informed by the high-dimensional patient’s physiological and clinical history. Our VIM parameters can be causally ...

Targeted Learning Of An Optimal Dynamic Treatment, And Statistical Inference For Its Mean Outcome, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose we observe n independent and identically distributed observations of a time-dependent random variable consisting of baseline covariates, initial treatment and censoring indicator, intermediate covariates, subsequent treatment and censoring indicator, and a final outcome. For example, this could be data generated by a sequentially randomized controlled trial, where subjects are sequentially randomized to a first line and second line treatment, possibly assigned in response to an intermediate biomarker, and are subject to right-censoring. In this article we consider estimation of an optimal dynamic multiple time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment ...