Statistics and Probability Commons^™

Estimation And Q-Matrix Validation For Diagnostic Classification Models, Yuling Feng

Theses and Dissertations

Diagnostic classification models (DCMs) are structured latent class models widely discussed in the field of psychometrics. They model subjects' underlying attribute patterns and classify subjects into unobservable groups based on their mastery of attributes required to answer the items correctly. The effective implementation of DCMs depends on correct specification of a Q-matrix which is a binary matrix linking attribute patterns to items. Current literature on assessing the appropriateness of Q-matrix specifications has focused on validation methods for the deterministic-input, noisy-and-gate (DINA) model. The goal of the study is to develop general Q-matrix validation methods that can be applied to a …

Protein Identification Using Bayesian Stochastic Search, Christina Nicole Lewis

Theses and Dissertations

Current methods for protein identification in tandem mass spectrometry (MS/MS) involve database searches or de novo peptide sequencing, with database searches being the standard method. With database searches, issues arise when the species is not in the database. Shortcomings of de novo peptide sequencing and database searches include chemical noise, overly complex fragments, and incomplete b and y ion sequences. Here we present a Bayesian approach to identifying peptides. Our model uses prior information about the average relative abundances of bond cleavages and the prior probability of any particular amino acid sequence. The proposed likelihood function is composed of two …

Modeling Mixed Unfolding/Monotone Dichotomous Item Exams, Na Yang

Theses and Dissertations

Item response theory (IRT) is widely applied to analyze educational and psychological assessments. Readily available IRT implementations allow for two common types of models: monotone models used for dominance scales (Guttman 1950; Rasch 1960/1980; Birnbaum 1968; Mokken 1971) and unfolding models used for proximity scales (Coombs, 1964; Andrich, 1996; Roberts, Donoghue and Laughlin, 2000).

When an exam contains items following both types of models, there is currently no method to distinguish the item types, estimate their characteristics, or estimate the examinee characteristics. Thus, there is no existing methodology to simultaneously analyze items like ``At a minimum, I am in favor …

Permutation Testing For Covariance Matrices, With Applications In Shape Analysis, Blake Cassidy Hill

Theses and Dissertations

In many applications, it is of interest to compare covariance structures. In this work, we propose hypothesis tests for comparing covariance matrices for data in different groups, especially in shape analysis. The main motivation for the work is comparing covariance matrices of the size and shapes of damaged versus undamaged DNA molecules. A practical motivation behind analyzing the differences between these DNA covariance matrices is to compare the variation between the two groups during situations where the molecules are repairing. The testing methods proposed in this dissertation consist of three types of permutation testing methods for differences in covariance structures. …

Models And Software Development For Interval-Censored Data, Chun Pan

Theses and Dissertations

Interval-censored time-to-event data occur naturally in studies of diseases where the symptoms are not directly observable, and periodic clinical examinations are required for detection. Due to the lack of well-established procedures, interval-censored data have been conventionally treated as right-censored data, however, this introduces bias at the first place. This dissertation focuses on methodological research and software development for interval-censored data. Specifically, it consists of three projects. The first project is to create an R package for regression analysis and survival curve estimation of interval-censored data based on several published papers by our research team. In the second project, a Bayesian …

Advanced Methodology Developments In Mixture Cure Models, Chao Cai

Theses and Dissertations

Modern medical treatments have substantially improved cure rates for many chronic diseases and have generated increasing interest in appropriate statistical models to handle survival data with non-negligible cure fractions. The mixture cure models are designed to model such data set, which assume that studied population is a mixture of being cured and uncured. In this dissertation, I will develop two programs named smcure and NPHMC in R. The first program aims to facilitate estimating two popular mixture cure models: the proportional hazards (PH) mixture cure model and accelerated failure time (AFT) mixture cure model. The second program focuses on designing …

A New Method For The Comparison Of Survival Distributions, Jaymie Shanahan

Theses and Dissertations

The assessment of overall homogeneity of time-to-event curves is a key element in survival analysis in biomedical research. The currently commonly used testing methods, e.g. log-rank test, Wilcoxon test, and Kolmogorov-Smirnov test, may have a significant loss of statistical testing power under certain circumstances. In this thesis we replicate a testing method (Lin & Xu, 2009) that is robust for the comparison of the overall homogeneity of survival curves based on the absolute difference of the area under the survival curves using normal approximation by Greenwood's formula, and propose a new weight component to their test statistic. The weight component …

Multiple Subject Barycentric Discriminant Analysis (Musubada): How To Assign Scans To Categories Without Using Spatial Normalization, Hervé Abdi, Lynne J. Williams, Andrew C. Connolly, M. Ida Gobbini

Dartmouth Scholarship

We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can …

Optimal Spatial Prediction Using Ensemble Machine Learning, Molly M. Davies, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Spatial prediction is an important problem in many scientific disciplines. Super Learner is an ensemble prediction approach related to stacked generalization that uses cross-validation to search for the optimal predictor amongst all convex combinations of a heterogeneous candidate set. It has been applied to non-spatial data, where theoretical results demonstrate it will perform asymptotically at least as well as the best candidate under consideration. We review these optimality properties and discuss the assumptions required in order for them to hold for spatial prediction problems. We present results of a simulation study confirming Super Learner works well in practice under a …

A Modular Mind? A Test Using Individual Data From Seven Primate Species, Federica Amici, Bradley Barney, Valen E. Johnson, Josep Call, Filippo Aureli

Faculty Articles

It has long been debated whether the mind consists of specialized and independently evolving modules, or whether and to what extent a general factor accounts for the variance in performance across different cognitive domains. In this study, we used a hierarchical Bayesian model to re-analyse individual level data collected on seven primate species (chimpanzees, bonobos, orangutans, gorillas, spider monkeys, brown capuchin monkeys and long-tailed macaques) across 17 tasks within four domains (inhibition, memory, transposition and support). Our modelling approach evidenced the existence of both a domain-specific factor and a species factor, each accounting for the same amount (17%) of the …

Relating Nanoparticle Properties To Biological Outcomes In Exposure Escalation Experiments, Trina Patel, Cecile Low-Kam, Zhaoxia Ji, Haiyuan Zhang, Tian Xia, Andre E. Nel, Jeffrey I. Zinc, Donatello Telesca

COBRA Preprint Series

A fundamental goal in nano-toxicology is that of identifying particle physical and chemical properties, which are likely to explain biological hazard. The first line of screening for potentially adverse outcomes often consists of exposure escalation experiments, involving the exposure of micro-organisms or cell lines to a battery of nanomaterials. We discuss a modeling strategy, that relates the outcome of an exposure escalation experiment to nanoparticle properties. Our approach makes use of a hierarchical decision process, where we jointly identify particles that initiate adverse biological outcomes and explain the probability of this event in terms of the particle physico-chemical descriptors. The …

Evaluation Of The Survival Effect For Various Treatment Modalities Among Stage Ii And Iii Rectal Cancer Patients In California, 1994-2009, Myung Mi Cho

Loma Linda University Electronic Theses, Dissertations & Projects

Background: European trials evaluating the effect of preoperative (PreOP) versus postoperative chemoradiotherapy (PostOP CRT) found no survival benefit. However, the effect of a change from PostOP to PreOP CRT has not been evaluated in a population-based setting. We sought to evaluate multimodal treatment changes and overall survival for perioperative (PeriOP) CRT versus surgery alone and for PreOP versus PostOP CRT from 1994 through 2009 among patients receiving radical surgery for stage II and III rectal cancer (RC).

Patients and Methods: We conducted a nonconcurrent cohort study evaluating demographic predictors of multimodal therapy for stage II and III RC using …

A Regionalized National Universal Kriging Model Using Partial Least Squares Regression For Estimating Annual Pm2.5 Concentrations In Epidemiology, Paul D. Sampson, Mark Richards, Adam A. Szpiro, Silas Bergen, Lianne Sheppard, Timothy V. Larson, Joel Kaufman

UW Biostatistics Working Paper Series

Many cohort studies in environmental epidemiology require accurate modeling and prediction of fine scale spatial variation in ambient air quality across the U.S. This modeling requires the use of small spatial scale geographic or “land use” regression covariates and some degree of spatial smoothing. Furthermore, the details of the prediction of air quality by land use regression and the spatial variation in ambient air quality not explained by this regression should be allowed to vary across the continent due to the large scale heterogeneity in topography, climate, and sources of air pollution. This paper introduces a regionalized national universal kriging …

Sensitivity Analysis For Causal Inference Under Unmeasured Confounding And Measurement Error Problems, Iván Díaz, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper we present a sensitivity analysis for drawing inferences about parameters that are not estimable from observed data without additional assumptions. We present the methodology using two different examples: a causal parameter that is not identifiable due to violations of the randomization assumption, and a parameter that is not estimable in the nonparametric model due to measurement error. Existing methods for tackling these problems assume a parametric model for the type of violation to the identifiability assumption, and require the development of new estimators and inference for every new model. The method we present can be used in …

Computationally Efficient Confidence Intervals For Cross-Validated Area Under The Roc Curve Estimates, Erin Ledell, Maya L. Petersen, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In binary classification problems, the area under the ROC curve (AUC), is an effective means of measuring the performance of your model. Most often, cross-validation is also used, in order to assess how the results will generalize to an independent data set. In order to evaluate the quality of an estimate for cross-validated AUC, we must obtain an estimate for its variance. For massive data sets, the process of generating a single performance estimate can be computationally expensive. Additionally, when using a complex prediction method, calculating the cross-validated AUC on even a relatively small data set can still require a …

A National Model Built With Partial Least Squares And Universal Kriging And Bootstrap-Based Measurement Error Correction Techniques: An Application To The Multi-Ethnic Study Of Atherosclerosis, Silas Bergen, Lianne Sheppard, Paul D. Sampson, Sun-Young Kim, Mark Richards, Sverre Vedal, Joel Kaufman, Adam A. Szpiro

UW Biostatistics Working Paper Series

Studies estimating health effects of long-term air pollution exposure often use a two-stage approach, building exposure models to assign individual-level exposures which are then used in regression analyses. This requires accurate exposure modeling and careful treatment of exposure measurement error. To illustrate the importance of carefully accounting for exposure model characteristics in two-stage air pollution studies, we consider a case study based on data from the Multi-Ethnic Study of Atherosclerosis (MESA). We present national spatial exposure models that use partial least squares and universal kriging to estimate annual average concentrations of four PM2.5 components: elemental carbon (EC), organic carbon (OC), …

An Analysis Of Risk Reduction Choices In Dcis Breast Cancer Patients, Lauren Soltesz

Statistics

The main focus of this paper was to evaluate possible demographic and clinical characteristics associated with a woman’s choice of breast conserving surgery (BCS), unilateral mastectomy (ULM), or bilateral risk reduction mastectomy (BRRM). The cohort consisted of patients presenting to the City of Hope National Medical Center with ductal carcinoma in situ breast cancer who elected to have cancer directed surgery (N=305). Analyses to examine associations of patient characteristics with type of surgery were conducted using a multinomial logistic regression. Results showed that older women were more likely to choose breast conserving surgery over bilateral risk reduction mastectomy than younger …

Oscillation Results For Fourth-Order Nonlinear Dynamic Equations, Chenghui Zhang, Tongxing Li, Ravi P. Agarwal, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. a new oscillation result and an example are included. © 2012 Elsevier Ltd. All rights reserved.

Jensen's Functionals On Time Scales, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić

Mathematics and Statistics Faculty Research & Creative Works

We consider Jensen's functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. by applying the properties of Jensen's functionals on these means, we obtain several refinements and converses of Hölder's inequality on time scales. Copyright © 2012 Matloob Anwar et al.

Analysis Of Alcohol Use Among Pregnant Women In San Luis Obispo County, Samantha Law

Statistics

Drinking alcohol during pregnancy is harmful to the fetus, and can lead to serious alcohol related developmental birth defects. Utilizing prenatal screening, such as the 4P’s Plus© screening tool, during a woman’s first prenatal doctors visit can help educate women and reduce continued alcohol use during pregnancy. Currently the CDC reports that 1 in 13 women in the US drink alcohol while pregnant compared to local reports that 1 in 3 women in San Luis Obispo County continue to drink alcohol during pregnancy. A primary concern for many local county health care experts and organizations is to raise awareness that …