Statistics and Probability Commons^™

An Inferential Framework For Network Hypothesis Tests: With Applications To Biological Networks, Phillip Yates

Theses and Dissertations

The analysis of weighted co-expression gene sets is gaining momentum in systems biology. In addition to substantial research directed toward inferring co-expression networks on the basis of microarray/high-throughput sequencing data, inferential methods are being developed to compare gene networks across one or more phenotypes. Common gene set hypothesis testing procedures are mostly confined to comparing average gene/node transcription levels between one or more groups and make limited use of additional network features, e.g., edges induced by significant partial correlations. Ignoring the gene set architecture disregards relevant network topological comparisons and can result in familiar n<

Estimation Of Causal Effects Of Community Based Interventions, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose one assigns two interventions to a small number K of different populations or communities, and one measures covariates and outcomes on a random sample of independent individuals from each of the K populations. We investigate the problem of identification and estimation of the causal effect of the choice of intervention assigned at the community level, and, if the intervention is time-dependent, the causal effect of the changes in the intervention at time t, on the outcome. The challenge one is confronted with is that different populations have different environmental factors and that the intervention and environment are assigned to …

Modeling Menstrual Cycle Length And Variability At The Approach Of Menopause Using Bayesian Changepoint Models, Xiaobi Huang, Michael R. Elliott, Sioban D. Harlow

The University of Michigan Department of Biostatistics Working Paper Series

As women approach menopause, the patterns of their menstruation cycle lengths change. To study these changes, we need to jointly model both the mean and variability of the cycle length. The model incorporates separate mean and variance change points for each woman and a hierarchical model to link them together, along with regression components to include predictors of menopausal onset such as age at menarche and parity. Data are from TREMIN, an ongoing 70-year old longitudinal study that has obtained menstrual calendar data of women throughout their reproductive life course. An additional complexity arises from the fact that these calendars …

Optimizing Randomized Trial Designs To Distinguish Which Subpopulations Benefit From Treatment, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes …

Multi-State Life Tables, Equilibrium Prevalence, And Baseline Selection Bias, Paula Diehr, David Yanez

UW Biostatistics Working Paper Series

Consider a 3-state system with one absorbing state, such as Healthy, Sick, and Dead. If the system satisfies the 1-step Markov conditions, the prevalence of the Healthy state will converge to a value that is independent of the initial distribution. This equilibrium prevalence and its variance are known under the assumption of time homogeneity, and provided reasonable estimates in the time non-homogeneous systems studied. Here, we derived the equilibrium prevalence for a system with more than three states. Under time homogeneity, the equilibrium prevalence distribution was shown to be an eigenvector of a partition of the matrix of transition probabilities. …

The Strength Of Statistical Evidence For Composite Hypotheses: Inference To The Best Explanation, David R. Bickel

COBRA Preprint Series

A general function to quantify the weight of evidence in a sample of data for one hypothesis over another is derived from the law of likelihood and from a statistical formalization of inference to the best explanation. For a fixed parameter of interest, the resulting weight of evidence that favors one composite hypothesis over another is the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function over the parameter of interest. Since the weight of evidence is generally only known up to a nuisance parameter, it is approximated by replacing the likelihood function with …

Approximation Of Stationary Statistical Properties Of Dissipative Dynamical Systems: Time Discretization, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We consider temporal approximation of stationary statistical properties of dissipative infinite-dimensional dynamical systems. We demonstrate that stationary statistical properties of the time discrete approximations, i.e., numerical scheme, converge to those of the underlying continuous dissipative infinite-dimensional dynamical system under three very natural assumptions as the time step approaches zero. the three conditions that are sufficient for the convergence of the stationary statistical properties are: (1) uniform dissipativity of the scheme in the sense that the union of the global attractors for the numerical approximations is pre-compact in the phase space; (2) convergence of the solutions of the numerical scheme to …

Investigating Relationships In The Flash Pilot Study For Stride, Mathew R. Adams, Katrina J. Jackson, Andrew J. Zbin

Statistics

No abstract provided.

Study Questions For Actuarial Exam 2/Fm, Aaron Hardiek

Statistics

No abstract provided.

Statistical Analysis Of Texas Holdem Poker, Daniel Bragonier

Statistics

Gathered lifetime online Poker data for Mike Linn. Attempted to analyze data to obtain information to maximize profit. Techniques included Univariate Analysis, Regression analysis, Anova analysis, Logistic Regression, and outlier Analysis. After the analysis, nothing of supreme importance or sustenance was found. Encountered issues with too much power. Results lead to plenty of statistical significance, but little practical significance. Results showed that the data did not provide all the answers that were being sought after, but there was some value in examining the data in a strict statistical manner.

Manova: Type I Error Rate Analysis, Kyle Wesley Gasperik

Statistics

Multivariate analysis of variance (MANOVA) is most commonly used in the field of bio-statistics. Throughout this paper I conduct numerous simulations that help analyze how robust the MANOVA procedure is against its assumptions. Using Type I error rate as my measure of error, I used the R software to graph my results. The main assumption that is focused on is the equal covariance matrix assumption, which we introduce correlation between variables to see how well the MANOVA procedure performs. Overall, 70 simulations were ran, and 10 functions were created to perform all of the analysis.

Improving The Teaching Of Econometrics At Pace University Using Stata, Gregory Colman

Cornerstone 3 Reports : Interdisciplinary Informatics

The goal of this grant was to improve the teaching of econometrics at Pace using the computer program, Stata, the most widely-used econometrics software among applied economists.

A Critical Constructionist View Of "At-Risk" Youth In Alternative Education, Rachelle Silverstein Touzard

Loma Linda University Electronic Theses, Dissertations & Projects

Family therapists and school counselors are increasingly called upon to provide services for youth in alternative education (Carver, Lewis, & Tice, 2010). Alternative education systems are programs for youth who have been defined as at risk. This study explored the at-risk discourse and asked the questions (a) how do youth and staff define the term at risk, (b) construct their experience in alternative education systems, and (c) experience their relationships with each other.

Combined elements from critical theory and a social constructionist perspective guided this study. A qualitative, grounded theory method was used that included semi structured interviews with …

Emergency Department Staff Adherence To Bad News Delivery Recommendations, Kristen R. Myers

Loma Linda University Electronic Theses, Dissertations & Projects

Emergency department (ED) staff is responsible for giving bad news regarding death, diagnoses, and other traumatic losses to patients and loved ones. Individuals receiving traumatic and sudden bad news are at increased risk of serious psychological and physiological consequences of disrupted grief. Despite published recommended practices for providers to help prevent maladaptive grief responses, little research is available on actual bad news delivery practices and factors promoting or hindering adherence to recommendations, and no study specifically explored the ED context.

The study used a qualitative design to explore bad news delivery practices, awareness of recommendations, factors perceived to hinder or …

The Textural Discontinuity Hypothesis And Its Relation To Nomadism, Migration, Decline, And Competition, Aaron L. Alai

School of Natural Resources: Dissertations, Theses, and Student Research

The causes of nomadism, migration, and decline in vertebrates are debated issues in the ecological sciences. Literature suggests nomadism may arise in species that specialize in granivory, nectivory, or the utilization of rodent outbreaks. Migration is thought to arise as a result of the exploitation of certain scarce or variable food resources. Species decline is hypothesized to be the result of many different factors as well; large species, island species and specialists may be more prone to decline.

A fresh perspective regarding the causes for species nomadism, migration, and decline is being investigated utilizing the ideas within the Textural Discontinuity …

The Teaching Of Equation Solving: Approaches In Standards-Based And Traditional Curricula In The United States, Jinfa Cai, Bikai Nie, John Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper discusses the approaches to teaching linear equation solving that are embedded in a Standards-based mathematics curriculum (Connected Mathematics Program or CMP) and in a traditional mathematics curriculum (Glencoe Mathematics) in the United States. Overall, the CMP curriculum takes a functional approach to teaching equation solving, while Glencoe Mathematics takes a structural approach. The functional approach emphasizes the important ideas of change and variation in situations and contexts. It also emphasizes the representation of relationships between variables. The structural approach, on the other hand, requires students to work abstractly with symbols and follow procedures in a systematic way. …

An Empirical Approach To Evaluating Sufficient Similarity: Utilization Of Euclidean Distance As A Similarity Measure, Scott Marshall

Theses and Dissertations

Individuals are exposed to chemical mixtures while carrying out everyday tasks, with unknown risk associated with exposure. Given the number of resulting mixtures it is not economically feasible to identify or characterize all possible mixtures. When complete dose-response data are not available on a (candidate) mixture of concern, EPA guidelines define a similar mixture based on chemical composition, component proportions and expert biological judgment (EPA, 1986, 2000). Current work in this literature is by Feder et al. (2009), evaluating sufficient similarity in exposure to disinfection by-products of water purification using multivariate statistical techniques and traditional hypothesis testing. The work of …

Model-Robust Regression And A Bayesian `Sandwich' Estimator, Adam A. Szpiro, Kenneth M. Rice, Thomas Lumley

UW Biostatistics Working Paper Series

The published version of this paper in Annals of Applied Statistics (Vol. 4, No. 4 (2010), 2099–2113) is available from the journal web site at http://dx.doi.org/10.1214/10-AOAS362.

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber-White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated …

Cost And Accuracy Comparisons In Medical Testing Using Sequential Testing Strategies, Anwar Ahmed

Theses and Dissertations

The practice of sequential testing is followed by the evaluation of accuracy, but often not by the evaluation of cost. This research described and compared three sequential testing strategies: believe the negative (BN), believe the positive (BP) and believe the extreme (BE), the latter being a less-examined strategy. All three strategies were used to combine results of two medical tests to diagnose a disease or medical condition. Descriptions of these strategies were provided in terms of accuracy (using the maximum receiver operating curve or MROC) and cost of testing (defined as the proportion of subjects who need 2 tests to …

The Use Of Propensity Scores To Assess The Generalizability Of Results From Randomized Trials, Elizabeth A. Stuart, Stephen R. Cole, Catherine P. Bradshaw, Philip J. Leaf

Johns Hopkins University, Dept. of Biostatistics Working Papers

Randomized trials remain the most accepted design for estimating the effects of interventions, but they do not necessarily answer a question of primary interest: Will the program be effective in a target population in which it may be implemented? In other words,are the results generalizable? There has been very little statistical research on how to assess the generalizability, or "external validity," of randomized trials. We propose the use of propensity-score-based metrics to quantify the similarity of the participants in a randomized trial and a target population. In this setting the propensity score model predicts participation in the randomized trial, given …

Powerful Snp Set Analysis For Case-Control Genome Wide Association Studies, Michael C. Wu, Peter Kraft, Michael P. Epstein, Deanne M. Taylor, Stephen J. Chanock, David J. Hunter, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Asymptotic Properties Of The Sequential Empirical Roc And Ppv Curves, Joseph S. Koopmeiners, Ziding Feng

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three common measures of performance for a diagnostic biomarker. The independent increments covariance structure assumption is common in the group sequential study design literature. Showing that summary measures of the ROC, PPV and NPV curves have an independent increments covariance structure will provide the theoretical foundation for designing group sequential diagnostic biomarker studies. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. In this paper we derive asymptotic theory …

The Linkset Model For 2^N Contingency Tables, Mikel Aickin

COBRA Preprint Series

Abstract The linkset model is defined for parametrizing the general 2^n contingency table. The linkset parameters are designed to represent latent influences that promote the co-occurrences of binary events beyond that explained by chance. Linkages involving 2 through n binary variables are included in this parametrization. The intent of this process is to elucidate the patterns of linkage, no matter how complex they might be, rather than to fit simplifying models. The relationship between linkset parameters and the natural parameters for a 2n table are derived, and large sample inference methods are provided. Examples are given from medical diagnostics, survival …

Estimating Causal Effects In Trials Involving Multi-Treatment Arms Subject To Non-Compliance: A Bayesian Frame-Work, Qi Long, Roderick J. Little, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Targeted Maximum Likelihood Estimator Of A Causal Effect On A Bounded Continuous Outcome, Susan Gruber, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Targeted maximum likelihood estimation of a parameter of a data generating distribution, known to be an element of a semiparametric model, involves constructing a parametric model through an initial density estimator with parameter epsilon representing an amount of fluctuation of the initial density estimator, where the score of this fluctuation model at epsilon=0 equals the efficient influence curve/canonical gradient. The latter constraint can be satisfied by many parametric fluctuation models, since it represents only a local constraint of its behavior at zero fluctuation. However, it is very important that the fluctuations stay within the semiparametric model for the observed data …

Super Learner In Prediction, Eric C. Polley, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Super learning is a general loss based learning method that has been proposed and analyzed theoretically in van der Laan et al. (2007). In this article we consider super learning for prediction. The super learner is a prediction method designed to find the optimal combination of a collection of prediction algorithms. The super learner algorithm finds the combination of algorithms minimizing the cross-validated risk. The super learner framework is built on the theory of cross-validation and allows for a general class of prediction algorithms to be considered for the ensemble. Due to the previously established oracle results for the cross-validation …

Second-Order Statistics Of Stochastic Electromagnetic Beams Propagating Through Non-Kolmogorov Turbulence, Elena Shchepakina, Olga Korotkova

Physics Articles and Papers

We present a detailed investigation, qualitative and quantitative, on how the atmospheric turbulence with a non-Kolmogorov power spectrum affects the major statistics of stochastic electromagnetic beams, such as the spectral composition and the states of coherence and polarization. We suggest a detailed survey on how these properties evolve on propagation of beams generated by electromagnetic Gaussian Schell-model sources, depending on the fractal constant α of the atmospheric power spectrum.

Assessing Noninferiority In A Three-Arm Trial Using The Bayesian Approach, Pulak Ghosh, Farouk S. Nathoo, Mithat Gonen, Ram C. Tiwari

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm clinical trial is usually recommended for non-inferiority trials by the Food and Drug Administration (FDA). The three-arm trial consists of a placebo, a reference, and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with …

Derivation Of Mass Independent Quantum Treatment Of Phenomenon, David Parker

Journal of Modern Applied Statistical Methods

The derivation and applications is presented of a spatial variable or spatial radius which is related to the inertia or mass-energy of any quantum body by a Lorentz invariant relation. Mass independent DeBroglie and Schroedinger equations are derived and applied to the resolution of the linguistic incompatibility between quantum theory and the geometrical weak equivalence principle. The equivalence principle is restated in terms of the spatial radius. The gravitational attraction between bodies and the relativistic energy are both presented in terms of the spatial radius follows. The ratio of the gravitational force to the Coulomb force at the Planck scale …

Ranked Set Sampling Using Auxiliary Variables Of A Randomized Response Procedure For Estimating The Mean Of A Sensitive Quantitative Character, Carlos N. Bouza

Journal of Modern Applied Statistical Methods

The analysis of the behavior of estimators of the mean of a sensitive variable is considered when a randomized response procedure is used. The results deal with the inference based on simple random sampling with replacement study design. A study of the behavior of the procedures for a ranked set sampling design is developed. A gain in accuracy is generally associated with the proposed alternative model.