Physical Sciences and Mathematics Commons^™

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 …

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 …

Development And Application Of Bayesian Semiparametric Models For Dependent Data, Junshu Bao

Theses and Dissertations

Dependent data are very common in many research fields, such as medicine (repeated measures), finance (time series), traffic (clustered), etc. Effective control/modeling of the dependency among data can enhance the performance of the models and result in better prediction. In many cases, the correlation itself may be of great interest. In this dissertation, we develop novel Bayesian semi-/nonparametric regression models to analyze data with various dependence structures. In Chapter 2, a Bayesian non- parametric multivariate ordinal regression model is proposed to fit drinking behavior survey data from DWI offenders. The responses are two-dimensional ordinal data, drinking frequency and drinking quantity …

Registration And Clustering Of Functional Observations, Zizhen Wu

Theses and Dissertations

As an important exploratory analysis, curves of similar shape are often classified into groups, which we call clustering of functional data. Phase variations or time distortions are often encountered in the biological processes, such as growth patterns or gene profiles. As a result of time distortion, curves of similar shape may not be aligned. Regular clustering methods for functional data usually ignore the presence of phase variations, which may result in low clustering accuracy. However, it is difficult to account for phase variation without knowing the cluster structure.

In this dissertation, we first propose a Bayesian method that simultaneously clusters …

Semiparametric Joint Dynamic Modeling Of A Longitudinal Marker, Recurrent Competing Risks, And A Terminal Event, Piaomu Liu

Theses and Dissertations

The joint modeling framework has found extensive applications in cancer and other biomedical research. For example, recent initiatives and developments in precision medicine call for appropriate prognostic tools to assist individualized or personalized approaches in cancer diagnosis and treatment. Data generated by clinical trials and medical research often include correlated longitudinal marker measurements and time- to-event information, which are possibly a recurrent event, competing risks, and a survival outcome. Primary interests of joint modeling include the association between the longitudinal marker measurements and time-to-event data, as well as predictions of survival probabilities of new observational units from the same population. …

Semiparametric Regression Analysis Of Panel Count Data And Interval-Censored Failure Time Data, Bin Yao

Theses and Dissertations

This dissertation discusses three important research topics on semiparametric regression analysis of panel count data and interval-censored data. Both types of data arise commonly in real-life studies in many fields such as epidemiology, social science, and medical research. In these studies, subjects are usually examined multiple times at periodical or irregular follow-up examinations. For panel count data, the response variable is the counts of some recurrent events, whose exact occurrence times are usually unknown. For interval-censored data, the response variable is the time to some events of interest, often called survival time or failure time, and the exact response time …

Frailty Probit Models For Clustered Interval-Censored Failure Time Data, Haifeng Wu

Theses and Dissertations

Survival analysis is an important branch of statistics that deals with time to event data or survival data. An important feature of such data is that the survival time of interest is usually not completely known but is censored due to the design of the study or an early dropout. In this dissertation we focus on studying clustered interval-censored data, a special type of survival data. Interval-censored data arise in many epidemiological, social science, and medical studies, in which subjects are examined at periodical follow-up visits. The survival (or failure) time of interest is never exactly observed but is known …

Bayesian Ensemble Of Regression Trees For Multinomial Probit And Quantile Regression, Bereket P. Kindo

Theses and Dissertations

This dissertation proposes multinomial probit Bayesian additive regression trees (MPBART), ordered multiclass Bayesian additive classification trees (O-MBACT) and Bayesian quantile additive regression trees (BayesQArt) as extensions of BART - Bayesian additive regression trees for tackling multinomial choice, multiclass classification, ordinal regression and quantile regression problems. The proposed models exhibit very good predictive performances. In particular, ranking among the top performing procedures when non-linear relationships exist between the response and the predictors. The proposed procedures can readily be applied on data sets with the number of predictors larger than the number of observations.

MPBART is sufficiently flexible to allow inclusion of …

Modern Estimation Problems In Group Testing, Md Shamim Sarker

Theses and Dissertations

In the simplest form of group testing, pools are formed by compositing a fixed number of individual specimens (e.g., blood, urine, swab, etc.) and then the pools are tested for a binary characteristic, such as presence or absence of a disease. Group testing is commonly used to screen for a variety of sexually transmitted diseases in epidemiological applications where the main goal is to increase testing efficiency. In this dissertation, we study three estimation problems that are motivated by real-life applications. We propose new methods to model group testing data for both single and multiple infections. In the first problem, …