Statistics and Probability Commons^™

Drawing Valid Targeted Inference When Covariate-Adjusted Response-Adaptive Rct Meets Data-Adaptive Loss-Based Estimation, With An Application To The Lasso, Wenjing Zheng, Antoine Chambaz, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Adaptive clinical trial design methods have garnered growing attention in the recent years, in large part due to their greater flexibility over their traditional counterparts. One such design is the so-called covariate-adjusted, response-adaptive (CARA) randomized controlled trial (RCT). In a CARA RCT, the treatment randomization schemes are allowed to depend on the patient’s pre-treatment covariates, and the investigators have the opportunity to adjust these schemes during the course of the trial based on accruing information (including previous responses), in order to meet a pre-specified optimality criterion, while preserving the validity of the trial in learning its primary study parameter.

In …

Negative Outcome Control For Unobserved Confounding Under A Cox Proportional Hazards Model, Eric J. Tchetgen Tchetgen, Tamar Sofer, David Richardson

Harvard University Biostatistics Working Paper Series

No abstract provided.

Review Of Developing Quantitative Literacy Skills In History And The Social Sciences: A Web-Based Common Core Approach By Kathleen W. Craver, Victor J. Ricchezza, H L. Vacher

Numeracy

Kathleen W. Craver. Developing Quantitative Literacy Skills in History and Social Sciences: A Web-Based Common Core Standards Approach (Lantham MD: Rowman & Littlefield Publishing Group, Inc., 2014). 191 pp.
ISBN 978-1-4758-1050-9 (cloth); ISBN …-1051-6 (pbk); ISBN…-1052-3 (electronic).

This book could be a breakthrough for teachers in the trenches who are interested in or need to know about quantitative literacy (QL). It is a resource providing 85 topical pieces, averaging 1.5 pages, in which a featured Web site is presented, described, and accompanied by 2-4 critical-thinking questions purposefully drawing on data from the Web site. The featured Web sites range from …

The Levels Of Conceptual Understanding In Statistics (Locus) Project: Results Of The Pilot Study, Douglas Whitaker, Steven Foti, Tim Jacobbe

Numeracy

The Levels of Conceptual Understanding in Statistics (LOCUS) project (NSF DRL-111868) has created assessments that measure conceptual (rather than procedural) understanding of statistics as outlined in GAISE Framework (Franklin et al., 2007, Guidelines for Assessment and Instruction in Statistics Education, American Statistical Association). Here we provide a brief overview of the LOCUS project and present results from multiple-choice items on the pilot administration of the assessments with data collected from over 3400 students in grades 6-12 across six states. These results help illustrate students’ understanding of statistical topics prior to the implementation of the Common Core State Standards. Using the …

Survival Analysis With Functions Of Mis-Measured Covariate Histories: The Case Of Chronic Air Pollution Exposure In Relation To Mortality In The Nurses' Health Study, Xiaomei Liao, Molin Wang, Jaime E. Hart, Francine Laden, Donna Spiegelman

Harvard University Biostatistics Working Paper Series

Environmental epidemiologists are often interested in estimating the effect of functions of time-varying exposure histories, such as the 12-month moving average, in relation to chronic disease incidence or mortality. The individual exposure measurements that comprise such an exposure history are usually mis-measured, at least moderately, and, often, more substantially. To obtain unbiased estimates of Cox model hazard ratios for these complex mis-measured exposure functions, an extended risk set regression calibration (RRC) method for Cox models is developed and applied to a study of long-term exposure to the fine particulate matter ($PM_{2.5}$) component of air pollution in relation to all-cause mortality …

Interdisciplinary Modeling For Water-Related Issues Graduate Course, Laurel Saito, Alexander Fernald, Timothy Link

All ECSTATIC Materials

The science and management of aquatic ecosystems is inherently interdisciplinary, with issues associated with hydrology, atmospheric science, water quality, geochemistry, sociology, economics, environmental science, and ecology. Addressing water resources issues in any one discipline invariably involves effects that concern other disciplines, and attempts to address one issue often have consequences that exacerbate existing issues or concerns, or create new ones (Jørgensen et al. 1992; Lackey et al. 1975; Straskraba 1994) due to the strongly interactive nature of key processes (Christensen et al. 1996). Thus, research and management of aquatic ecosystems must be interdisciplinary to be most effective, but such truly …

Nitrate And Nitrite Ingestion And Risk Of Ovarian Cancer Among Postmenopausal Women In Iowa, Maki Inoue-Choi, Rena R. Jones, Kristin E. Anderson, Kenneth P. Cantor, James R. Cerhan, Stuart Krasner, Kimberly Robien, Peter J. Weyer, Mary H. Ward

Epidemiology Faculty Publications

Nitrate and nitrite are precursors in the endogenous formation of N-nitroso compounds (NOC), potential human carcinogens. We evaluated the association of nitrate and nitrite ingestion with postmenopausal ovarian cancer risk in the Iowa Women's Health Study. Among 28,555 postmenopausal women, we identified 315 incident epithelial ovarian cancers from 1986 to 2010. Dietary nitrate and nitrite intakes were assessed at baseline using food frequency questionnaire data. Drinking water source at home was obtained in a 1989 follow-up survey. Nitrate-nitrogen (NO₃-N) and total trihalomethane (TTHM) levels for Iowa public water utilities were linked to residences and average levels were …

Characterizations Of Levy Distribution Via Sub-Independence Of The Random Variables And Truncated Moments, Gholamhossein G. Hamedani, M. Ahsanullah, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In …

Missing Photos, Suffering Withdrawal, Or Finding Freedom? How Experiences Of Social Media Non-Use Influence The Likelihood Of Reversion, Eric P.S. Baumer, Shion Guha, Emily Quan, David Mimno, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article examines social media reversion, when a user intentionally ceases using a social media site but then later resumes use of the site. We analyze a convenience sample of survey data from people who volunteered to stay off Facebook for 99 days but, in some cases, returned before that time. We conduct three separate analyses to triangulate on the phenomenon of reversion: simple quantitative predictors of reversion, factor analysis of adjectives used by respondents to describe their experiences of not using Facebook, and statistical topic analysis of free-text responses. Significant factors predicting either increased or decreased likelihood of reversion …

Size And Power Of Tests Of Hypotheses On Survival Parameters From The Lindley Distribution With Covariates, Macaulay Okwuokenye, Karl E. Peace

Biostatistics: Faculty Publications

The Lindley model is considered as an alternative model facilitating analyses of time-to-event data with covariates. Covariate information is incorporated using the Cox’s proportional hazard model with the Lindley model at the timedependent component. Simulation studies are performed to assess the size and power of tests of hypotheses on parameters arising from maximum likelihood estimators of parameters in the Lindley model. Results are contrasted with that arising from Cox’s partial maximum likelihood estimator. The Linley model is used to analyze a publicly available data set and contrasted with other models.

Joint Modeling Of Treatment Effect On Time-To-Event Endpoint And Safety Covariates In Control Clinical Trial Data Analysis, Kao-Tai Tsai, Karl E. Peace

Biostatistics: Faculty Publications

It is a common practice to perform a separate analysis of efficacy and safety data from clinical trials to estimate the benefit and risk aspects of a particular treatment regimen. However, by doing so, one is likely to miss the complete picture of the treatment effect given that these data are generated from the same study subjects and therefore most likely will be correlated. Therefore, it is desirable to analyze these data jointly to obtain a more complete profile of the treatment regimen. A substantial number of statistical methodologies have been proposed in the last decade to model the time-to-event …

Data And Analytics In Corporate Real Estate: Do You Have The Right Talent?, Clarence Goh

Research Collection School Of Accountancy

Is the lack of suitable data and analytics talent in your corporate real estate (CRE) team preventing you from contributing to the wider business strategy?

High Impact Strategies And The Effect It Has On Students’ Mathematics Attitudes, Lauren A. Ryba

All Student Theses and Dissertations

This study was designed to determine if innovative strategies such as the use of technology and Supplemental Instruction (SI) could have an impact on students in an introductory statistics course. The study describes the use of a reliable instrument to measure students’ attitudes and beliefs about mathematics. Martha Tapia developed the Attitudes Toward Mathematics Inventory (ATMI) instrument in 1996 and later Lim and Chapman further refined a short form in 2012. The purpose of the ATMI was to measure mathematics attitudes in four ways: (1) enjoyment of mathematics, (2) motivation to do mathematics, (3) self confidence in mathematics, and (4) …

Supervised Classification Using Copula And Mixture Copula, Sumen Sen

Mathematics & Statistics Theses & Dissertations

Statistical classification is a field of study that has developed significantly after 1960's. This research has a vast area of applications. For example, pattern recognition has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rule assumes normality. However in many situations, this assumption is often questionable. In fact for some data, the pattern vector is a mixture of discrete and continuous random variables. In this dissertation, we use copula densities to model class conditional distributions. Such types of densities are useful when the marginal densities of a pattern vector are not normally …

Fast, Accurate, And Reliable Molecular Docking With Quickvina 2, Amr Alhossary, Stephanus Daniel Handoko, Yuguang Mu, Chee-Keong Kwoh

Research Collection School Of Computing and Information Systems

Motivation: The need for efficient molecular docking tools for high-throughput screening is growing alongside the rapid growth of drug-fragment databases. AutoDock Vina ('Vina') is a widely used docking tool with parallelization for speed. QuickVina ('QVina 1') then further enhanced the speed via a heuristics, requiring high exhaustiveness. With low exhaustiveness, its accuracy was compromised. We present in this article the latest version of QuickVina ('QVina 2') that inherits both the speed of QVina 1 and the reliability of the original Vina.Results: We tested the efficacy of QVina 2 on the core set of PDBbind 2014. With the default exhaustiveness level …

Doubly Robust Estimation Of A Marginal Average Effect Of Treatment On The Treated With An Instrumental Variable, Lan Liu, Wang Miao, Baoluo Sun, James M. Robins, Eric J. Tchetgen Tchetgen

Harvard University Biostatistics Working Paper Series

No abstract provided.

Thyroid Autoimmunity As A Window To Autoimmunity: An Explanation For Sex Differences In The Prevalence Of Thyroid Autoimmunity, Stephen Merrill, Ying Mu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Autoimmune thyroid diseases (AITDs), predominately Graves׳ disease and Hashimoto׳s thyroiditis, comprise the most common autoimmune diseases in humans. Both have the production of anti-thyroid antibody as an important aspect and both are much more prevalent in females, being at least 10 times more common than in males. Using these two clues, a hypothesis for the initiation of thyroid autoimmunity is proposed that helps to make the case that the thyroid is one of the most sensitive sites for autoimmunity and helps account for the prevalence and the observed sex differences in AITDs and associated diseases, such as type 1 diabetes …

One-Step Targeted Minimum Loss-Based Estimation Based On Universal Least Favorable One-Dimensional Submodels, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Consider a study in which one observes n independent and identically distributed random variables whose probability distribution is known to be an element of a particular statistical model, and one is concerned with estimation of a particular real valued pathwise differentiable target parameter of this data probability distribution. The canonical gradient of the pathwise derivative of the target parameter, also called the efficient influence curve, defines an asymptotically efficient estimator as an estimator that is asymptotically linear with influence curve equal to the efficient influence curve.The targeted maximum likelihood estimator is a two stage estimator obtained by constructing a so …

Parental Involvement, Students' Self-Engagement, And Academic Achievement: A Structural Equation Model, Cuirong Wu

Electronic Theses and Dissertations

In the ever-evolving landscape of China's education system, the gap between the rural and urban was always an important issue, not only the multifaceted interplay of parental involvement, student self-engagement, and academic performance. This study utilized a comprehensive national survey dataset through a thorough understanding of cultural nuances and educational intricacies specific to the Chinese context. Its aim was not only to decipher the underlying constructs of parental involvement and student self-engagement but also to investigate how these factors impacted academic achievement among students. The research unfolded in several stages using a representative sample of 10750 students from 112 schools …

Penalized Function-On-Function Regression, Andrada Ivanescu, Ana Maria Staicu, Fabian Scheipl, Sonja Greven

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A general framework for smooth regression of a functional response on one or multiple functional predictors is proposed. Using the mixed model representation of penalized regression expands the scope of function-on-function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed on the same or different domains than the functional response, on a dense or sparse grid, and with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the …

On Stochastic Comparisons Of Largest Order Statistics In The Scale Model, Subhash C. Kochar, Nuria Torrado

Mathematics and Statistics Faculty Publications and Presentations

Let X-lambda 1, X-lambda 2, ... ,X-lambda n be independent non negative random variables with X-lambda i similar to F(lambda(i)t), i = 1, ... , n, where lambda(i) > 0, i = 1, ... , n and F is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic X-n:n(lambda) n is smaller than another one X-n:n(theta) according to likelihood ratio ordering. Furthermore, we apply these results when F is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases.

Time Series Analysis For Psychological Research: Examining And Forecasting Change, Andrew T. Jebb, Louis Tay, Wei Wang, Qiming Huang

Publications and Research

Psychological research has increasingly recognized the importance of integrating temporal dynamics into its theories, and innovations in longitudinal designs and analyses have allowed such theories to be formalized and tested. However, psychological researchers may be relatively unequipped to analyze such data, given its many characteristics and the general complexities involved in longitudinal modeling. The current paper introduces time series analysis to psychological research, an analytic domain that has been essential for understanding and predicting the behavior of variables across many diverse fields. First, the characteristics of time series data are discussed. Second, different time series modeling techniques are surveyed that …

Identification And Doubly Robust Estimation Of Data Missing Not At Random With An Ancillary Variable, Wang Miao, Eric Tchetgen Tchetgen, Zhi Geng

Harvard University Biostatistics Working Paper Series

No abstract provided.

Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, Catalin Barboianu

UNLV Gaming Research & Review Journal

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of mathematical modeling, arguing that such …

Advanced Topics In Experimental Design, Jason Anderson

Statistics

No abstract provided.

Generating Random Vectors Using Transformation With Multiple Roots And Its Applications, Qidi Peng, Henry Schellhorn, Lu Zhu

Applications and Applied Mathematics: An International Journal (AAM)

An approach is proposed to generate random vectors using transformation with multiple roots. This approach generalizes the one-dimensional inverse transformation with multiple roots method to higher dimensions, i.e., to random vectors with or without densities. In this approach, multiple roots of the transformation and probabilities of selecting each of the roots are derived. The strategies for constructing such a transformation are discussed and several examples are presented to motivate this simulation approach.

A Note On An M/M/S Queueing System With Two Reconnect And Two Redial Orbits, Amina A. Bouchentouf, Hanane Sakhi

Applications and Applied Mathematics: An International Journal (AAM)

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new …

Strong Uniform Consistency Of Hazard Function With Functional Explicatory Variable In Single Functional Index Model Under Censored Data, Omar Belabbaci, Abbes Rabhi, Sara Soltani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we deal with nonparametric estimate of the conditional hazard function, when the covariate is functional. Kernel type estimators for the conditional hazard function of a scalar response variable Y given a Hilbertian random variable X are introduced, where the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the kernel estimate of this model in various situations, including censored and non-censored data. The rates of convergence emphasize the crucial role played by the small ball probabilities with respect to the distribution of …

Estimation Of The Parameters Of Exponential Distribution Using Top-K-Lists, M. Ahsanullah, Mohamed Habibullah

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the estimation of location and scale parameters of the exponential distribution based on top-k-list of a sequence of observations from a two parameter exponential distribution. The minimum variance unbiased estimates of the location and scale parameters are given. Some comparisons of the variances of these estimates with respect to that of the kth record values are given.

Analysis Of Repairable M[X]/(G1,G2)/1 - Feedback Retrial G-Queue With Balking And Starting Failures Under At Most J Vacations, P. Rajadurai, M. C. Saravanarajan, V. M. Chandrasekaran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of services and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them get into the orbit. The negative customer, is arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters the orbit or leaves the system. If the orbit is empty at the service completion of each type …