Statistics and Probability Commons^™

A Logistic L-Moment-Based Analog For The Tukey G-H, G, H, And H-H System Of Distributions, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper introduces a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric γ-κ, (ii) log-logistic γ, (iii) symmetric κ, and (iv) asymmetric κL-κR. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavy-tailed distributions are of interest. A procedure is also described for simulating γ-κ, γ, κ, and κL-κR distributions with specified L-moments and L-correlations. The …

Murine Gut Microbiota Is Defined By Host Genetics And Modulates Variation Of Metabolic Traits, Autumn M. Mcknite, Maria Elisa Perez-Munoz, Lu Lu, Evan G. Williams, Simon Brewer, Penelope A. Andreux, John W. M. Bastiaansen, Xusheng Wang, Stephen D. Kachman, Johan Auwerx, Robert W. Williams, Andrew K. Benson, Daniel A. Peterson, Daniel C. Ciobanu

Department of Statistics: Faculty Publications

The gastrointestinal tract harbors a complex and diverse microbiota that has an important role in host metabolism. Microbial diversity is influenced by a combination of environmental and host genetic factors and is associated with several polygenic diseases. In this study we combined next-generation sequencing, genetic mapping, and a set of physiological traits of the BXD mouse population to explore genetic factors that explain differences in gut microbiota and its impact on metabolic traits. Molecular profiling of the gut microbiota revealed important quantitative differences in microbial composition among BXD strains. These differences in gut microbial composition are influenced by host-genetics, which …

Foundations Of Inference, Kevin H. Knuth, John Skilling

Physics Faculty Scholarship

We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information.

On The Existence Of Constant Accrual Rates In Clinical Trials And Direction For Future Research, Byron J. Gajewski, Stephen D. Simon, Susan E. Carslon

Byron J Gajewski

Many clinical trials fall short of their accrual goals. This can be avoided with accurate accrual prediction tools. Past researchers provide important methodological alternative models for predicting accrual in clinical trials. One model allows for slow accrual at the start of the study, which eventually reaches a threshold. A simpler model assumes a constant rate of accrual. A comparison has been attempted but we wish to point out some important considerations when comparing these two models. In fact, we can examine the reasonableness of a constant accrual assumption (simpler model) which had data 239 days into a three- year study. …

Estimation Of The Effects Of Parental Measures On Child Aggression Using Structural Equation Modeling, Jordan Daniel Pyper

Theses and Dissertations

A child's parents are the primary source of knowledge and learned behaviors for developing children, and the benefits or repercussions of certain parental practices can be long lasting. Although parenting practices affect behavioral outcomes for children, families tend to be diverse in their circumstances and needs. Research attempting to ascertain cause and effect relationships between parental influences and child behavior can be difficult due to the complex nature of family dynamics and the intricacies of real life. Structural equation modeling (SEM) is an appropriate method for this research as it is able to account for the complicated nature of child-parent …

On Identification Of Natural Direct Effects When A Confounder Of The Mediator Is Directly Affected By Exposure, Eric J. Tchetgen Tchetgen, Tyler J. Vanderweele

COBRA Preprint Series

Natural direct and indirect effects formalize traditional notions of mediation analysis into a rigorous causal framework and have recently received considerable attention in epidemiology and in the social sciences. Sufficient conditions for identification of natural direct effects were formulated by Judea Pearl under a nonparametric structural equations model, which assumes certain independencies between potential outcomes. A common situation in epidemiology is that a confounder of the mediator is affected by the exposure, in which case, natural direct effects fail to be nonparametrically identified without additional assumptions, even under Pearl's nonparametric structural equations model. In this paper, the authors show that …

Selective Impact Of Hiv Disease Progression On The Innate Immune System In The Human Female Reproductive Tract., Timothy Lahey, Mimi Ghosh, John V. Fahey, Zheng Sheng, Lucy R. Mukura, Yan Song, Susan Cu-Uvin, Kenneth H. Mayer, Peter F. Wright, John C. Kappes, Christina Ochsenbauer, Charles R. Wira

Epidemiology Faculty Publications

Background

We have previously demonstrated intrinsic anti-HIV activity in cervicovaginal lavage (CVL) from HIV-infected women with high CD4 counts and not on antiretroviral therapy. However, the impact of HIV disease progression on CVL innate immune responses has not been delineated.

Methods

CVL from 57 HIV-infected women not on antiretroviral therapy were collected by washing the cervicovaginal area with 10 ml of sterile normal saline. We characterized subject HIV disease progression by CD4 count strata: >500 cells/µl, 200–500 cells/µl, or <200 cells/µl of blood. To assess CVL anti-HIV activity, we incubated TZM-bl cells with HIV plus or minus CVL. Antimicrobials, cytokines, chemokines and anti-gp160 HIV IgG antibodies were measured by ELISA and Luminex.

Results

CVL exhibited broad anti-HIV activity against multiple laboratory-adapted and transmitted/founder (T/F) viruses, with anti-HIV activity ranging from 0 to 100% …

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Analysis Of Dietary Patterns Over Freshman Year Of College, Chelsea Lofland

Statistics

This analysis is an investigation of changes in Cal Poly students’ eating habits over freshman year. The motivation behind this was an interest in college students’ lifestyles; college is the first time most students live on their own and it can be an important maturation period. College is stressful, exciting, liberating, and terrifying all at the same time. This distinctive life experience, along with my desire to handle big and messy data, led me to this research question.

The response variable analyzed was food consumption and the explanatory variables were: sex, race, quarter, food group, stress, exercise, BMI, sleep quality …

Lifestyle Choices In Relation To Bmi And Blood Pressure, Shawna Perry

Statistics

Cal Poly currently has one of the largest ongoing university health studies in the United States. Launched in Fall 2009, the Cal Poly FLASH study, led by the Kinesiology department and STRIDE, is a longitudinal study that tracks the classes of 2013 and 2014 through online surveys and physical assessments. The data collected covers various areas such as perceived health, lifestyle choices, and actual physical health.

My project analyzed the FLASH data to investigate the relationship between various perceived variables and actual health measures for Cal Poly freshmen. The motivation for this analysis was an interest in both diet and …

Predictors Of Hypertension And Prehypertension In Cal Poly Students, Toria Mock

Statistics

This study analyzed predictors of hypertension and prehypertension in Cal Poly students. Hypertension and prehypertension are known to increase the risk of blood clots, plaque buildup, and tissue/organ damage from blocked arteries. Researching predictors of hypertension and prehypertension can help to determine methods of minimizing the probability of hypertension and prehypertension in a patient. Data from the FLASH study was used to analyze associations between possible predictor variables, such as stress and physical activity, and hypertension/prehypertension. BMI, bodyfat, and the interaction between videogames per weekend day and gender were found to be significantly associated with hypertension and prehypertension in Cal …

Blunt Impact Performance Evaluation Of Helmet Lining Systems For Military And Recreational Use, Jaclyn Siniora, Ryan Taylor, Darren Suey

Industrial Technology and Packaging

With the increasing problem in collegiate athletes experiencing injuries to the brain, different helmet liners where put to the test to see which liner provided athletes the greatest protection under specific conditions.

This senior project evaluates five different liners in football helmets. Each of the helmet liners were tested at three different temperatures: hot, cold, and ambient. Each helmet had seven different impact locations which were put to the test. The project was designed to be used to test ACH military combat liners as well. Due to shipping bottle necks the ACH combat liners have been left to future Cal …

Involvement Of Microrna Families In Cancer, Stefan Wuchty, Dolores Arjona, Serdar Bozdag, Peter O. Bauer

Mathematics, Statistics and Computer Science Faculty Research and Publications

Collecting representative sets of cancer microRNAs (miRs) from the literature we show that their corresponding families are enriched in sets of highly interacting miR families. Targeting cancer genes on a statistically significant level, such cancer miR families strongly intervene with signaling pathways that harbor numerous cancer genes. Clustering miR family-specific profiles of pathway intervention, we found that different miR families share similar interaction patterns. Resembling corresponding patterns of cancer miRs families, such interaction patterns may indicate a miR family’s potential role in cancer. As we find that the number of targeted cancer genes is a naı¨ve proxy for a cancer …

Change-Point Analysis Of Paired Allele-Specific Copy Number Variation Data, Yinglei Lai

GW Biostatistics Center

The recent genome-wide allele-specific copy number variation data enable us to explore two types of genomic information including chromosomal genotype variations as well as DNA copy number variations. For a cancer study, it is common to collect data for paired normal and tumor samples. Then, two types of paired data can be obtained to study a disease subject. However, there is a lack of methods for a simultaneous analysis of these four sequences of data. In this study, we propose a statistical framework based on the change-point analysis approach. The validity and usefulness of our proposed statistical framework are demonstrated …

Characteristics Of Children With Type 1 Diabetes And Persistent Suboptimal Glycemic Control., Hyuntae Kim, Angelo Elmi, Celia L. Henderson, Fran R. Cogen, Paul B. Kaplowitz

Epidemiology Faculty Publications

Objective: This study aims to determine the relationship between the duration of persistent poor glycemic control in type 1 diabetes mellitus (T1DM) children and the likelihood of subsequent improvement.

Methods: A retrospective cohort study was conducted on T1DM patients aged 6-18 years, followed for at least six visits at Children’s National Medical Center (Washington, DC) with at least one hemoglobin A1c (HbA1c) ≥10% after the first year since the initial visit (n=151). Medical records of patients with subsequently improved glycemic control were reviewed (n=39).

Results: Patients aged 12-18 years, females, and Medicaid patients were twice as likely to be in …

Analysing Domestic Electricity Smart Metering Data Using Self Organising Maps, Fintan Mcloughlin, Aidan Duffy, Michael Conlon

Conference Papers

This paper investigates a method of classifying domestic electricity load profiles through Self Organising Maps (SOMs). Approximately four thousand customers are divided into groups based on their electricity demand patterns. Dwelling and occupant characteristics are then investigated for each group. The results show that SOMs are an effective way of classifying customers into groups in terms of their electrical load profile and that certain dwelling and occupant characteristics are significant factors in determining which group they end up in.

Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah

Applications and Applied Mathematics: An International Journal (AAM)

Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, …

Rank-Based Estimation And Prediction For Mixed Effects Models In Nested Designs, Yusuf K. Bilgic

Dissertations

Hierarchical designs frequently occur in many research areas. The experimental design of interest is expressed in terms of fixed effects but, for these designs, nested factors are a natural part of the experiment. These nested effects are generally considered random and must be taken into account in the statistical analysis. Traditional analyses are quite sensitive to outliers and lose considerable power to detect the fixed effects of interest.

This work proposes three rank-based fitting methods for handling random, fixed and scale effects in k-level nested designs for estimation and inference. An algorithm, which iteratively obtains robust prediction for both scale …

Improvement Of Statistical Process Control At St. Jude Medical's Cardiac Manufacturing Facility, Christopher Lance Edwards

Master's Theses

Sig sigma is a methodology where companies strive to reproduce results ending up having a 99.9996% chance their product will be void of defects. In order for companies to reach six sigma, statistical process control (SPC) needs to be introduced. SPC has many different tools associated with it, control charts being one of them. Control charts play a vital role in managing how a process is behaving. Control charts allow users to identify special causes, or shifts, and can therefore change the process to keep producing good products, free of defects.

There are many factories and manufacturing facilities having implemented …

Computing Highly Accurate Or Exact P-Values Using Importance Sampling, Chris Lloyd

Chris J. Lloyd

Especially for discrete data, standard first order P-values can suffer from poor accuracy, even for quite large sample sizes. Moreover, different test statistics can give practically different results. There are several approaches to computing P-values which do not suffer these defects, such as parametric bootstrap P-values or the partially maximised P-values of Berger and Boos (1994).

Both these methods require computing the exact tail probability of the approximate P-value as a function of the nuisance parameter/s, known as the significance profile. For most practical problems, this is not computationally feasible. I develop an importance sampling approach to this problem. A …