Physical Sciences and Mathematics Commons^™

Topics In Group Testing With Multiple Infections, Peijie Hou

Theses and Dissertations

Group testing, dating back to the early 1940s, was first proposed to screen for syphilis among US inductees during World War II (Dorfman, 1943). Since then, the benefits of reducing testing costs by employing group testing have been demonstrated in many areas, such as drug discovery, genetics, and infectious disease testing. Traditionally, statistical research in group testing has largely been motivated by applications involving a single infection. With the recent development of multiplex assays that can diagnose multiple infections simultaneously, generalizing the existing group testing literature to incorporate multiple infections is a natural and necessary next step. This dissertation consists …

Bayesian Flexible Modeling Of Interval-Censored Failure Time Data, Sheng-Yang Wang

Theses and Dissertations

Interval-censored data are a special type of survival data, in which the survival time is not accurately observed but known to fall within a specific time interval. Interval censored data commonly arise in real-life epidemiological and medical studies that involve periodic examinations. In this dissertation, several semi-parametric regression models are investigated to provide flexible modeling and robust inference for interval censored data from Bayesian perspectives.

Chapter 1 provides a detailed description about interval-censored data and gives several examples. Existing models and methods for analyzing such interval-censored data are reviewed as well. Chapter 2 develops a unified Bayesian estimation approach under …

Semiparametric Estimation And Inference In Causal Inference And Measurement Error Models, Jianxuan Liu

Theses and Dissertations

This dissertation research has focused on theoretical and practical developments of semiparametric modeling and statistical inference for high dimensional data and measurement error data. In causal inference framework, when evaluating the effectiveness of medical treatments or social intervention policies, the average treatment effect becomes fundamentally important. We focus on propensity score modelling in treatment effect problems and develop new robust tools to overcome the curse of dimensionality. Furthermore, estimating and testing the effect of covariates of interest while accommodating many other covariates is an important problem in many scientific practices, including but not limited to empirical economics, public health and …

Longitudinal And Geographical Modeling Of Circular Data With An Application To Sudden Infant Death Syndrome, Xinyan Cai

Theses and Dissertations

The aim of this thesis is to study seasonality of death in U.S. infants who died from SIDS. We also propose to investigate secular trends and geographical patterns of seasonal patterns of mortality. The application of circular statistics is used to describe the seasonality of the month of death in infants who died from SIDS in 1990, 2000 and 2010. The secular trends of seasonal patterns of SIDS mortality are investigated using a circular linear regression model after adjusting for potential confounders. The geographical variation in seasonal patterns of SIDS mortality is explored from the U.S. map and quantified by …

Statistical Methods For Multivariate And Correlated Data, Xinling Xu

Theses and Dissertations

A commonly encountered data type in real life is count data, especially in selfreported behavioral studies. One issue of the self-reported count data is the inaccuracy. In the first part of the dissertation, we are going to address one specific type of inaccuracy in bivariate count data–heaping. Copula functions are used for the formulation of the bivariate distribution. Using copula functions for solving data inaccuracy problems is still a new area, which we are going to explore in this dissertation.

We also discuss the methods for variable selection when the explanatory variables are highly correlated. In particular, our method is …

Evaluation Of Goodness-Of-Fit Tests For The Cox Proportional Hazards Model With Time-Varying Covariates, Shanshan Hong

Theses and Dissertations

The proportional hazards (PH) model, proposed by Cox (1972), is one of the most popular survival models for analyzing time-to-event data. To use the PH model properly, one must examine whether the data satisfy the PH assumption. An alternative model should be suggested if the PH assumption is invalid. The main purpose of this thesis is to examine the performance of five existing methods for assessing the PH assumption. Through extensive simulations, the powers of five different existing methods are compared; these methods include the likelihood ratio test, the Schoenfeld residuals test, the scaled Schoenfeld residuals test, Lin et al. …

Marginal Structural Cox Model For Survival Data With Treatment-Confounder Feedback, Yanan Zhang

Theses and Dissertations

In an observational longitudinal study, there can be time-varying exposure/treatment and time-varying confounders. When the confounders affect the exposure and prior exposure also has an impact on levels of confounders, there is treatment confounder feedback. To admit estimation of unbiased causal effects, these conditions need to be hold, exchangeability, positivity, consistency. The traditional method of conditioning on potential confounders does not meet these 3 conditions. Therefore, parameter estimates from traditional Cox model are biased casual effect estimates when the treatment confounder feedback exists. The marginal structural Cox model can be used to address this issue. By calculating and including inverse …

Functional Data Smoothing Methods And Their Applications, Songqiao Huang

Theses and Dissertations

In many subjects such as psychology, geography, physiology or behavioral science, researchers collect and analyze non-traditional data, i.e., data that do not consist of a set of scalar or vector observations, but rather a set of sequential observations measured over a fine grid on a continuous domain, such as time, space, etc. Because the underlying functional structure of the individual datum is of interest, Ramsay and Dalzell (1991) named the collection of topics involving analyzing these functional observations functional data analysis (FDA). Topics in functional data analysis include data smoothing, data registration, regression analysis with functional responses, cluster analysis on …

Improved Simultaneous Estimation Of Location And System Reliability Via Shrinkage Ideas, Beidi Qiang

Theses and Dissertations

In decision theory, when several parameters need to be estimated simultaneously, many standard estimators can be improved, in terms of a combined loss function. The problem of finding such estimators has been well studied in the literature, but mostly under parametric settings, which is inappropriate for heavy-tailed distributions. In the first part of this dissertation, a robust simultaneous estimator of location is proposed using the shrinkage idea. A nonparametric Bayesian estimator is also discussed as an alternative. The proposed estimators do not assume a specific parametric distribution and they do not require the existence of finite moments. The performance of …

Nonparametric Inference For Orderings And Associations Between Two Random Variables, Chuan-Fa Tang

Theses and Dissertations

Ordering and dependency are two aspects to describe the relationship between two random variables. In this thesis, we choose two hypothesis testing problems to tackle; i.e., a goodness-of-fit test for uniform stochastic ordering and one for positive quadrant dependence. For the test for uniform stochastic ordering, we propose new nonparametric tests based on ordinal dominance curves. We derive the limiting distributions of test statistics and provide the least favorable configuration to determine critical values. Numerical evidence is presented to support our theoretical results, and we apply our methods to a real data set. An extension for random right-censored data is …