Digital Commons Network^™

Individualized Predictions Of Disease Progression Following Radiation Therapy For Prostate Cancer., Jeremy Taylor, Menggang Yu, Howard M. Sandler

The University of Michigan Department of Biostatistics Working Paper Series

Background: Following treatment for localized prostate cancer, men are monitored with serial PSA measurements. Refining the predictive value of post-treatment PSA determinations may add to clinical management and we have developed a model that predicts for an individual patient future PSA values and estimates the time to future clinical recurrence.

Methods: Data from 934 patients treated for prostate cancer between 1987 and 2000 were used to develop a comprehensive statistical model to fit the clinical recurrence events and pattern of PSA data. A logistic regression model was used for the probability of cure, non-linear hierarchical mixed models were used for …

Multiple Imputation For Interval Censored Data With Auxiliary Variables, Chiu-Hsieh Hsu, Jeremy Taylor, Susan Murray

The University of Michigan Department of Biostatistics Working Paper Series

We propose a nonparametric multiple imputation scheme, NPMLE imputation, for the analysis of interval censored survival data. Features of the method are that it converts interval-censored data problems to complete data or right censored data problems to which many standard approaches can be used, and the measures of uncertainty are easily obtained. In addition to the event time of primary interest, there are frequently other auxiliary variables that are associated with the event time. For the goal of estimating the marginal survival distribution, these auxiliary variables may provide some additional information about the event time for the interval censored observations. …

Piecewise Constant Cross-Ratio Estimation For Association In Bivariate Survival Data With Application To Studying Markers Of Menopausal Transition, Bin Nan, Xihong Lin, Lynda D. Lisabet, Sioban Harlow

The University of Michigan Department of Biostatistics Working Paper Series

A question of significant interest in female reproductive aging is to identify bleeding criteria for the menopausal transition. Although various bleeding criteria, or markers, have been proposed for the menopausal transition, their validity has not been adequately examined. The Tremin Trust data are collected from a long-term cohort study that followed a group of women throughout their whole reproductive life, and provide a unique opportunity for assessing the association between age at onset of a bleeding marker and age onset of menopause. Formal statistical analysis of this dependence is challenging give the fact that both the marker event and menopause …

Individual Prediction In Prostate Cancer Studies Using A Joint Longitudinal-Survival-Cure Model, Menggang Yu, Jeremy Taylor, Howard M. Sandler

The University of Michigan Department of Biostatistics Working Paper Series

For monitoring patients treated for prostate cancer, Prostate Specific Antigen (PSA) is measured periodically after they receive treatment. Increases in PSA are suggestive of recurrence of the cancer and are used in making decisions about possible new treatments. The data from studies of such patients typically consist of longitudinal PSA measurements, censored event times and baseline covariates. Methods for the combined analysis of both longitudinal and survival data have been developed in recent years, with the main emphasis being on modeling and estimation. We analyze data from a prostate cancer study that has been extended by adding a mixture structure …

Mixture Models For Assessing Differential Expression In Complex Tissues Using Microarray Data, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

The use of DNA microarrays has become quite popular in many scientific and medical disciplines, such as in cancer research. One common goal of these studies is to determine which genes are differentially expressed between cancer and healthy tissue, or more generally, between two experimental conditions. A major complication in the molecular profiling of tumors using gene expression data is that the data represent a combination of tumor and normal cells. Much of the methodology developed for assessing differential expression with microarray data has assumed that tissue samples are homogeneous. In this article, we outline a general framework for determining …

Optimal Sample Size For Multiple Testing: The Case Of Gene Expression Microarrays, Peter Muller, Giovanni Parmigiani, Christian Robert, Judith Rousseau

Johns Hopkins University, Dept. of Biostatistics Working Papers

We consider the choice of an optimal sample size for multiple comparison problems. The motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression. However, the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests. We discuss two decision problems in the context of this setup: the sample size selection and the decision about the multiple comparisons. We adopt a decision theoretic approach,using loss functions that combine the competing goals of discovering as many ifferentially expressed genes as possible, while keeping …

No News Is Bad News: Characteristics Of Adolescents Who Provide Neither Parental Consent Nor Refusal For Participation In School-Based Survey Research, C. Anderson Johnson, Jennifer B. Unger, Peggy E. Gallaher, Paula Palmer, Lourdes Baezconde-Garbanati, Dennis R. Trinidad, Steven Cen

CGU Faculty Publications and Research

Schools offer a convenient setting for research on adolescents.However, obtaining active written parental consent is difficult. In a 6th-grade smoking study, students were recruited with two consent procedures: active consent (parents must provide written consent for their children to participate) and implied consent (children may participate unless their parents provide written refusal). Of 4,427 invited students, 3,358 (76%) provided active parental consent, 420 (9%) provided active parental refusal, and 649 (15%) provided implied consent (parental nonresponse). The implied consent procedure recruited more boys, African Americans, students with poor grades, and smokers. This dual-consent procedure is useful for collecting some limited …

An Analysis Of The Periodicity Of The Cell Cycle And Apoptotic Regulatory Proteins In Prostate Xenografts Using Anova And Cosinor Methods, Aleen Hosdaghian

Theses

Circadian rhythms have been found in both plants and animals, in normal tissues as well as in most tumors and human cancers. By following these rhythms in healthy and cancerous tissue, it has been possible to find optimal times to deliver a dose of drug, such that efficacy is maximized and toxicity to normal tissues is minimized. In this study, the periodicity of several cell cycle and apoptotic regulatory proteins were studied in two prostate cancer models against a dietary therapeutic agent, Selenium. The ALVA-3 1 (androgen-independent) and PC-3 (androgen-independent) prostate cancer cell lines were grown in vivo, as a …

Calibrating Observed Differential Gene Expression For The Multiplicity Of Genes On The Array, Yingye Zheng, Margaret S. Pepe

UW Biostatistics Working Paper Series

In a gene expression array study, the expression levels of thousands of genes are monitored simultaneously across various biological conditions on a small set of subjects. One goal of such studies is to explore a large pool of genes in order to select a subset of genes that appear to be differently expressed for further investigation. Of particular interest here is how to select the top k genes once genes are ranked based on their evidence for differential expression in two tissue types. We consider statistical methods that provide a more rigorous and intuitively appealing selection process for k. We …

Incorporating Death Into Health-Related Variables In Longitudinal Studies, Paula Diehr, Laura Lee Johnson, Donald L. Patrick, Bruce Psaty

UW Biostatistics Working Paper Series

Background: The aging process can be described as the change in health-related variables over time. Unfortunately, simple graphs of available data may be misleading if some people die, since they may confuse patterns of mortality with patterns of change in health. Methods have been proposed to incorporate death into self-rated health (excellent to poor) and the SF-36 profile scores, but not for other variables.

Objectives: (1) To incorporate death into the following variables: ADLs, IADLs, mini-mental state examination, depressive symptoms, body mass index (BMI), blocks walked per week, bed days, hospitalization, systolic blood pressure, and the timed walk. (2) To …

Overlap Bias In The Case-Crossover Design, With Application To Air Pollution Exposures, Holly Janes, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

The case-crossover design uses cases only, and compares exposures just prior to the event times to exposures at comparable control, or “referent” times, in order to assess the effect of short-term exposure on the risk of a rare event. It has commonly been used to study the effect of air pollution on the risk of various adverse health events. Proper selection of referents is crucial, especially with air pollution exposures, which are shared, highly seasonal, and often have a long term time trend. Hence, careful referent selection is important to control for time-varying confounders, and in order to ensure that …

Value Orientations And Opinions Of Recently Arrived Cubans In Miami, Andy S. Gomez, Eugenio M. Rothe

Institute for Cuban & Cuban-American Studies Occasional Papers

No abstract provided.

Multiple Solutions For Quasilinear Elliptic Neumann Problems In Orlicz-Sobolev Spaces, Nikolaos Halidias, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (ϕ-Laplacians). We are interested in Neumann boundary value problems and our main tool is Brézis-Nirenberg's local linking theorem.

Tid And See Testing Results Of Altera Cyclone Field Programmable Gate Array, Stephen L. Clark, K. Avery, R. Parker

Mathematics and Statistics Faculty Research & Creative Works

Total ionizing dose (TID) and single event effects testing was performed on Altera Cyclone FPGAs. The devices exhibit slight performance degradation to a TID of 1 Mrad (Si), but also exhibited single event latchup at a low LET.

Hereditarily Unicoherent Continua And Their Absolute Retracts, J. J. Charatonik, W. J. Charatonik, Janusz R. Prajs

Mathematics and Statistics Faculty Research & Creative Works

We investigate absolute retracts for classes of hereditarily unicoherent continua, tree-like continua, λ- dendroids, dendroids and some other related ones. The main results are: (1) the inverse limits of trees with confluent bonding mappings are absolute retracts of hereditarily unicoherent continua; (2) each tree-like continuum is embeddable in a special way in a tree-like absolute retract for the class of hereditarily unicoherent continua; (3) a dendroid is an absolute retract for hereditarily unicoherent continua if and only if it can be embedded as a retract into the Mohler-Nikiel universal smooth dendroid.

Existence And Comparison Results For Quasilinear Evolution Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu

Mathematics and Statistics Faculty Research & Creative Works

We generalize the sub-supersolution method known for weak solutions of single and multivalued nonlinear parabolic problems to quasilinear evolution hemivariational inequalities. To this end we first introduce our basic notion of sub- and supersolutions on the basis of which we then prove existence, comparison, compactness and extremality results for the hemivariational inequalities under considerations.

Oscillation Of Second Order Nonlinear Dynamic Equations On Time Scales, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.

Oscillation Theory For Second Order Dynamic Equations [Book Review], Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Multiple Testing. Part Iii. Procedures For Control Of The Generalized Family-Wise Error Rate And Proportion Of False Positives, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard

U.C. Berkeley Division of Biostatistics Working Paper Series

The accompanying articles by Dudoit et al. (2003b) and van der Laan et al. (2003) provide single-step and step-down resampling-based multiple testing procedures that asymptotically control the family-wise error rate (FWER) for general null hypotheses and test statistics. The proposed procedures fundamentally differ from existing approaches in the choice of null distribution for deriving cut-offs for the test statistics and are shown to provide asymptotic control of the FWER under general data generating distributions, without the need for conditions such as subset pivotality. In this article, we show that any multiple testing procedure (asymptotically) controlling the FWER at level alpha …

Cr Approximation On A Nonrigid Hypersurface Graph In Cⁿ, Al Boggess, Roman Dwilewicz

Mathematics and Statistics Faculty Research & Creative Works

Let M be a hypersurface in Cⁿ that is the graph over a (2n - 1)-linear real space. the main result of the paper is that any CR function on M can be uniformly approximated on compact subsets by entire functions on Cⁿ.

The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare

Mathematics and Statistics Faculty Research & Creative Works

We show that there are characters of compact, connected, nonabelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.

Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan

Articles and Preprints

In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.

Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley

Pomona Faculty Publications and Research

Motivation: Standard laboratory classification of the plasma cell dyscrasia monoclonal gammopathy of undetermined significance (MGUS) and the overt plasma cell neoplasm multiple myeloma (MM) is quite accurate, yet, for the most part, biologically uninformative. Most, if not all, cancers are caused by inherited or acquired genetic mutations that manifest themselves in altered gene expression patterns in the clonally related cancer cells. Microarray technology allows for qualitative and quantitative measurements of the expression levels of thousands of genes simultaneously, and it has now been used both to classify cancers that are morphologically indistinguishable and to predict response to therapy. It is …

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Reconstructability Analysis With Fourier Transforms, Martin Zwick

Complex Systems Faculty Publications and Presentations

Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the Fourier approach is also …

Controlling Wound Healing Through Debridement, M. A. Jones, Baojun Song, D. M. Thomas

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

The formation of slough (dead tissue) on a wound is widely accepted as an inhibitor to natural wound healing. In this article, a system of differential equations that models slough/wound interaction is developed. We prove a threshold theorem that provides conditions on the amount of slough to guarantee wound healing. As a state-dependent time scale, debridement (the periodic removal of slough) is used as a control. We show that closure of the wound can be reached in infinite time by debriding.

Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam

Department of Math & Statistics Faculty Publications

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) …

A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam

Department of Math & Statistics Faculty Publications

As an alternative to traditional life testing, degradation tests can be effective in assessing product reliability when measurements of degradation leading to failure can be observed. This article presents a degradation model for highly reliable light displays, such as plasma display panels and vacuum fluorescent displays (VFDs). Standard degradation models fail to capture the burn-in characteristics of VFDs, when emitted light actually increases up to a certain point in time before it decreases (or degrades) continuously. Random coefficients are used to model this phenomenon in a nonlinear way, which allows for a nonmonotonic degradation path. In many situations, the relative …

Gamma-Set Domination Graphs. I: Complete Biorientations Of Q-Extended Stars And Wounded Spider Graphs, Kim A. S. Factor

Mathematics, Statistics and Computer Science Faculty Research and Publications

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, dom_γ(G) is created. All γ-sets of specific trees T are found, and dom-_γ(T) is characterized for those classes.

การทดสอบสมมติฐานเกี่ยวกับความเป็นอิสระของตัวแบบล็อกการิทึมเชิงเส้นที่มีการแจกแจงพหุนาม, ประกาศิต สิงคะตีระ

Chulalongkorn University Theses and Dissertations (Chula ETD)

การวิจัยครั้งนี้มีวัตถุประสงค์ เพื่อเปรียบเทียบวิธีการทดสอบสมมติฐานเกี่ยวกับความเป็นอิสระของตัวแปรเชิงกลุ่ม 3 ตัวแปร ในตารางการณ์จร 3 ทาง ขนาด 2x2x2 และศึกษาความเป็นไปได้ที่จะนำวิธีการมอนติคาร์โลมาใช้แทนวิธีการทดสอบด้วยตัวสถิติอัตราส่วนภาวะน่าจะเป็น วิธีการทดสอบที่นำมาศึกษาเปรียบเทียบมี 3 วิธี ได้แก่ วิธีการทดสอบด้วยตัวสถิติอัตราส่วนภาวะน่าจะเป็น วิธีการทดสอบด้วยตัวสถิติของเซลเทอร์แมนและวิธีมอนติคาร์โล โดยวิธีการมอนติคาร์โลเป็นวิธีการทดสอบสมมติฐานที่ไม่อาศัยค่าวิกฤติของตัวสถิติทดสอบ แต่จะทำการเปรียบเทียบค่าสถิติที่คำนวณได้จากข้อมูลตัวอย่างที่ต้องการศึกษากับค่าสถิติที่คำนวณได้จากข้อมูลเทียมแต่ละชุดที่จำลองขึ้นโดยการสุ่มตัวอย่างซ้ำภายใต้ข้อกำหนดตามสมมติฐานว่าง เพื่อนำไปสู่การหาค่า P-value ผู้วิจัยได้ทำการศึกษาในแต่ละตัวแบบที่เป็นไปได้และเป็นตัวแบบที่มีรูปแบบปิดของค่าความถี่คาดหวัง เพื่อให้สามารถจำลองข้อมูลได้ถูกต้อง ซึ่งตัวแบบต่างๆ ประกอบด้วยตัวแบบที่เป็นอิสระอย่างสมบูรณ์ ตัวแบบความเป็นอิสระร่วม และตัวแบบความเป็นอิสระอย่างมีเงื่อนไข และได้กำหนดระดับความสัมพันธ์ให้กับตัวแปรร่วมที่มีความสัมพันธ์ร่วมกัน จากน้อยไปหามากคือ 0.25, 0.50 และ 0.75 ขนาดตัวอย่างที่ใช้คือ 40, 60, 80, 120, 160, 200 และ 240 และระดับนัยสำคัญที่ใช้คือ 0.05 และ 0.01 เกณฑ์ที่ใช้ในการเปรียบเทียบคือการพิจารณาความสามารถในการควบคุมความน่าจะเป็นของความผิดพลาดประเภทที่ 1 และ ค่าอำนาจการทดสอบ การวิจัยครั้งนี้ได้จำลองข้อมูลโดยกระทำซ้ำแบบเทคนิคมอนติคาร์โล (Monte Carlo simulation technique) จำนวน 500 ครั้ง ซึ่งในแต่ละครั้งจะกระทำซ้ำแบบมอนติคาร์โลอีก 500 ครั้ง เพื่อสร้างชุดข้อมูล 500 ชุด เพื่อคำนวณค่า P-value ของวิธีการทดสอบแบบมอนติคาร์โล ผลการวิจัยสามารถสรุปได้ดังนี้ วิธีการทดสอบทั้ง 3 วิธีสามารถควบคุมความน่าจะเป็นของความผิดพลาดประเภทที่ 1 ได้ในทุกสถานการณ์ วิธีการมอนติคาร์โลมีแนวโน้มที่จะให้ค่าอำนาจการทดสอบสูงที่สุด รองลงมาคือวิธีการทดสอบด้วยตัวสถิติอัตราส่วนภาวะน่าจะเป็น และวิธีการสอบด้วยตัวสถิติของเซลเทอร์แมน และโดยเฉพาะอย่างยิ่งในกรณีตัวอย่างขนาดเล็ก วิธีการมอนติคาร์โลจะมีค่าอำนาจการทดสอบสูงกว่าวิธีการอื่นอย่างชัดเจน ทั้งนี้เนื่องจากแนวคิดของวิธีการมอนติคาร์โลที่มีการจำลองข้อมูลเทียมหลายชุดภายใต้สมมติฐานว่างขึ้นมาพิจารณานั้นเสมือนเป็นการสร้างขอบเขตที่เป็นไปได้ของข้อมูลตามข้อกำหนดในสมมติฐานว่าง เพื่อเปรียบเทียบกับข้อมูลตัวอย่างที่ศึกษา จึงมีความถูกต้องมากกว่าการทดสอบสมมติฐานโดยทั่วไปซึ่งเป็นการเปรียบเทียบระหว่างค่าสถิติที่คำนวณได้กับค่าวิกฤติเพียงครั้งเดียว นอกจากนี้ยังพบว่าค่าอำนาจการทดสอบของวิธีการทดสอบทั้ง 3 วิธีแปรผันตามขนาดตัวอย่าง ระดับความสัมพันธ์ของตัวแปรร่วม และระดับนัยสำคัญ โดยสรุป ผู้วิจัยพบว่ามีความเป็นไปได้ที่จะนำเอาการทดสอบสมมติฐานด้วยวิธีการมอนติคาร์โลมาใช้ทดสอบสมมติฐานเกี่ยวกับความเป็นอิสระของตัวแบบล็อกการิทึมเชิงเส้น แทนการทดสอบทั้งสองวิธีดังกล่าวใน 3 ตัวแบบข้างต้นได้ โดยเฉพาะอย่างยิ่งในกรณีตัวอย่างขนาดเล็ก