Statistics and Probability Commons^™

Asymptotic Theory For Three Infinite Dimensional Diffusion Processes, Youzhou Zhou

Open Access Dissertations and Theses

This thesis is centered around three infinite dimensional diffusion processes:

(i). the infinitely-many-neutral-alleles diffusion model [Ethier and Kurtz, 1981],

(ii). the two-parameter infinite dimensional diffusion model [Petrov, 2009] and [Feng and Sun, 2010],

(iii). the infinitely-many-alleles diffusion with symmetric dominance [Ethier and Kurtz, 1998].

The partition structures, the ergodic inequalities and the asymptotic theory of these three models are discussed. In particular, the asymptotic theory turns out to be the major contribution of this thesis.

In Chapter 2, a slightly altered version of Kingman's one-to-one correspondence theorem on partition structures is provided, which in turn becomes a handy tool ...

Likelihood-Based Inferential Methods For Some Flexible Cure Rate Models, Suvra Pal

Open Access Dissertations and Theses

Recently, the Conway-Maxwell Poisson (COM-Poisson) cure rate model has been proposed which includes as special cases some of the well-known cure rate models discussed in the literature. Data obtained from cancer clinical trials are often right censored and the expectation maximization (EM) algorithm can be efficiently used for the determination of the maximum likelihood estimates (MLEs) of the model parameters based on right censored data.

By assuming the lifetime distribution to be exponential, lognormal, Weibull, and gamma, the necessary steps of the EM algorithm are developed for the COM-Poisson cure rate model and some of its special cases. The inferential ...

Nutrition, Childhood Development And Prevalence Of Anemia In Ghanaian Children: Analysis Of Health Survey, Joycelyne E. Ewusie

Open Access Dissertations and Theses

Malnutrition and Anemia in children continue to be major public health challenges in most developing countries, particularly in Africa. Malnutrition and Anemia pervade all aspects of their health, growth, cognitive and social development. They lead to irreversible and lifelong effects that prevent children from realising their full potential. This study was designed to examine the prevalence and determinants of malnutrition and anemia in children under 5 years of age in the Ghanaian population. This research is based on data from the Ghana Demographic and Health Survey (GDHS) 2008, obtained from the Ghana Statistical Service (GSS). The survey is an extensive ...

Interpretation And Prediction Of A Logistic Model, Joseph M. Hilbe

Joseph M Hilbe

A basic overview of how to model and interpret a logistic regression model, as well as how to obtain the predicted probability or fit of the model and calculate its confidence intervals. R code used for all examples; some Stata is provided as a contrast.

Mediation Analysis With Time-Varying Exposures And Mediators, Tyler J. Vanderweele, Eric Tchetgen Tchetgen

Harvard University Biostatistics Working Paper Series

In this paper we consider mediation analysis when exposures and mediators vary over time. We give non-parametric identification results, discuss parametric implementation, and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models. We also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models. When there are no time-varying confounders affected by prior exposure and mediator values, identification of direct and indirect effects is achieved by a longitudinal version of Pearl's mediation formula. When there are time-varying confounders ...

Massively Parallel Nonparametric Regression, With An Application To Developmental Brain Mapping, Philip T. Reiss, Lei Huang, Yin-Hsiu Chen, Lan Huo, Thaddeus Tarpey, Maarten Mennes

Philip T. Reiss

We propose a penalized spline approach to performing large numbers of parallel nonparametric analyses of either of two types: restricted likelihood ratio tests of a parametric regression model versus a general smooth alternative, and nonparametric regression. Compared with naively performing each analysis in turn, our techniques reduce computation time dramatically. Viewing the large collection of scatterplot smooths produced by our methods as functional data, we develop a clustering approach to summarize and visualize these results. Our approach is applicable to ultra-high-dimensional data, particularly data acquired by neuroimaging; we illustrate it with an analysis of developmental trajectories of functional connectivity at ...

The Art Of Personal Science, Jeff Fajans

The STEAM Journal

Quantified Self isn’t really about finding answers or solving problems—it’s about asking new questions.

Toward Directed Energy Planetary Defense, Philip Lubin, Gary Hughes, Johanna Bible, Jesse Bublitz, Josh Arriola, Caio Motta, Jon Suen, Isabella Johansson, Jordan Riley, Nilou Sarvian, Deborah Clayton-Warwick, Jane Wu, Andrew Milich, Mitch Oleson, Mark Pryor, Peter Krogen, Miikka Kangas, Hugh O'Neill

Statistics

Asteroids and comets that cross Earth’s orbit pose a credible risk of impact, with potentially severe disturbances to Earth and society. We propose an orbital planetary defense system capable of heating the surface of potentially hazardous objects to the vaporization point as a feasible approach to impact risk mitigation. We call the system DE-STAR, for Directed Energy System for Targeting of Asteroids and exploration. The DESTAR is a modular-phased array of kilowatt class lasers powered by photovoltaics. Modular design allows for incremental development, minimizing risk, and allowing for technological codevelopment. An orbiting structure would be developed in stages. The ...

Variational Inference For Heteroscedastic Semiparametric Regression, Marianne Menictas, Matt Wand

Matt Wand

No abstract provided.

Variable-Domain Functional Regression, Jonathan E. Gellar, Elizabeth Colantuoni, Dale M. Needham, Ciprian M. Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

We introduce a class of scalar-on-function regression models with subject-specific functional predictor domains. The fundamental idea is to consider a bivariate functional parameter that depends both on the functional argument and on the width of the functional predictor domain. Both parametric and nonparametric models are introduced to fit the functional coefficient. The nonparametric model is theoretically and practically invariant to functional support transformation, or support registration. Methods were motivated by and applied to a study of association between daily measures of the Intensive Care Unit (ICU) Sequential Organ Failure Assessment (SOFA) score and two outcomes: in-hospital mortality, and physical impairment ...

Computational Model For Survey And Trend Analysis Of Patients With Endometriosis : A Decision Aid Tool For Ebm, Salvo Reina, Vito Reina, Franco Ameglio, Mauro Costa, Alessandro Fasciani

COBRA Preprint Series

Endometriosis is increasingly collecting worldwide attention due to its medical complexity and social impact. The European community has identified this as a “social disease”. A large amount of information comes from scientists, yet several aspects of this pathology and staging criteria need to be clearly defined on a suitable number of individuals. In fact, available studies on endometriosis are not easily comparable due to a lack of standardized criteria to collect patients’ informations and scarce definitions of symptoms. Currently, only retrospective surgical stadiation is used to measure pathology intensity, while the Evidence Based Medicine (EBM) requires shareable methods and correct ...

Adaptive Pair-Matching In The Search Trial And Estimation Of The Intervention Effect, Laura Balzer, Maya L. Petersen, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In randomized trials, pair-matching is an intuitive design strategy to protect study validity and to potentially increase study power. In a common design, candidate units are identified, and their baseline characteristics used to create the best n/2 matched pairs. Within the resulting pairs, the intervention is randomized, and the outcomes measured at the end of follow-up. We consider this design to be adaptive, because the construction of the matched pairs depends on the baseline covariates of all candidate units. As consequence, the observed data cannot be considered as n/2 independent, identically distributed (i.i.d.) pairs of units ...

Concomitant Socioeconomic, Behavioral, And Biological Factors Associated With The Disproportionate Hiv Infection Burden Among Black Men Who Have Sex With Men In 6 U.S. Cities, Kenneth H. Mayer, Lei Wang, Beryl A. Koblin, Sharon B. Mannheimer, Manya Magnus, +13 Additional Authors

Epidemiology and Biostatistics Faculty Publications

Background

American Black men who have sex with men (MSM) are disproportionately affected by HIV, but the factors associated with this concentrated epidemic are not fully understood.

Methods

Black MSM were enrolled in 6 US cities to evaluate a multi-component prevention intervention, with the current analysis focusing on the correlates of being newly diagnosed with HIV compared to being HIV-uninfected or previously diagnosed with HIV.

Results

HPTN 061 enrolled 1553 Black MSM whose median age was 40; 30% self-identified exclusively as gay or homosexual, 29% exclusively as bisexual, and 3% as transgender. About 1/6th(16.2%) were previously diagnosed ...

Adaptive Randomized Trial Designs That Cannot Be Dominated By Any Standard Design At The Same Total Sample Size, Michael Rosenblum

Johns Hopkins University, Dept. of Biostatistics Working Papers

Prior work has shown that certain types of adaptive designs can always be dominated by a suitably chosen, standard, group sequential design. This applies to adaptive designs with rules for modifying the total sample size. A natural question is whether analogous results hold for other types of adaptive designs. We focus on adaptive enrichment designs, which involve preplanned rules for modifying enrollment criteria based on accrued data in a randomized trial. Such designs often involve multiple hypotheses, e.g., one for the total population and one for a predefined subpopulation, such as those with high disease severity at baseline. We ...

A Joint Model For Multistate Disease Processes And Random Informative Observation Times, With Applications To Electronic Medical Records Data, Jane M. Lange, Rebecca A. Hubbard, Lurdes Y. T. Inoue, Vladimir Minin

UW Biostatistics Working Paper Series

Multistate models are used to characterize individuals' natural histories through diseases with discrete states. Observational data resources based on electronic medical records pose new opportunities for studying such diseases. However, these data consist of observations of the process at discrete sampling times, which may either be pre-scheduled and non-informative, or symptom-driven and informative about an individual's underlying disease status. We have developed a novel joint observation and disease transition model for this setting. The disease process is modeled according to a latent continuous time Markov chain; and the observation process, according to a Markov-modulated Poisson process with observation rates ...

Change Point Testing In Logistic Regression Models With Interaction Term, Youyi Fong, Chongzhi Di, Sallie Permar

UW Biostatistics Working Paper Series

The threshold effect takes place in situations where the relationship between an outcome variable and a predictor variable changes as the predictor value crosses a certain threshold/change point. Threshold effects are often plausible in a complex biological system, especially in defining immune responses that are protective against infections such as HIV-1, which motivates the current work. We study two hypothesis testing problems in change point models. We first compare three different approaches to obtaining a p-value for the maximum of scores test in a logistic regression model with change point variable as a main effect. Next, we study the ...

Simulating Univariate And Multivariate Tukey G-And-H Distributions Based On The Method Of Percentiles, Tzu-Chun Kou, Todd C. Headrick

Todd Christopher Headrick

This paper derives closed-form solutions for the 𝑔-and-ℎ shape parameters associated with the Tukey family of distributions based on the method of percentiles (MOP). A proposed MOP univariate procedure is described and compared with the method of moments (MOM) in the context of distribution fitting and estimating skew and kurtosis functions. The MOP methodology is also extended from univariate to multivariate data generation. A procedure is described for simulating nonnormal distributions with specified Spearman correlations. The MOP procedure has an advantage over the MOM because it does not require numerical integration to compute intermediate correlations. Simulation results demonstrate that the ...

Errata And Comments For Methods Of Statistical Model Estimation, Joseph M. Hilbe, Andew P. Robinson

Joseph M Hilbe

Errata and comments for Hilbe and Robinson's Methods of Statistical Model Estimation, Chapman & Hall/CRC (2013)

An Exploration Of “Non-Economic” Damages In Civil Jury Awards, Herbert M. Kritzer, Guangya Liu, Neil Vidmar

Faculty Scholarship

Using three primary data sources plus three supplemental sources discussed in an appendix, this paper examines how well non-economic damages could be predicted by economic damages and at how the ratio of non-economic damages to economic damages changed as the magnitude of the economic damages awarded by juries increased. We found a mixture of consistent and inconsistent patterns across our various datasets. One fairly consistent pattern was the tendency for the ratio of non-economic to economic damages to decline as the amount of economic damages increased. Moreover, the variability of the ratio also tended to decline as the amount of ...

Graphical Assessment Of Internal And External Calibration Of Logistic Regression Models Using Loess Smoothers, Peter C. Austin

Peter C Austin

Predicting the probability of the occurrence of a binary outcome or condition is important in biomedical research. While assessing discrimination is an essential issue in developing and validating binary prediction models, less attention has been paid to methods for assessing model calibration. Calibration refers to the degree of agreement between observed and predicted probabilities, and is often assessed by testing lack-of-fit. The objective of our study was to examine the ability of graphical methods to assess calibration of logistic regression models. We examined lack of internal calibration, which was related to mis-specification of the logistic regression model, and lack of ...