Thesis (M.Ag.Sc.) -- The Dept. of Biometry, University of Adelaide, Biometry Section, Waite Agricultural Research Institute, 1977.

Thesis (Ph.D.)--Virginia Commonwealth University, 2008. / Prepared for: Dept. of Biostatistics. Title from title-page of electronic thesis. Advisor: Kellie J. Archer. Bibliography: leaves 127-134.

Thesis (Ph.D.)--Virginia Commonwealth University, 2008. / Prepared for: Dept. of Biostatistics. Advisor: Kellie J. Archer. Bibliography: leaves 127-134. Also available online via the Internet.

Thesis (PH.D.)--Syracuse University, 2003. / "Publication number AAT 3081640."

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (PH.D.) -- Syracuse University, 2006 / "Publication number AAT 3242507."

The longitudinal data analysis plays an important role in a lot of applications today. It is defined by many measurements are obtained over many times. These measurements has complicated correlation structure because they are obtained from the same subjects over the time. In multivariate longitudinal data, there is an additional source of correlation which is "outcomes", the data are obtained over the time for many outcomes for the same subjects. This application could happens in many medical, financial and psychological studies. For example, the patients measurements for some variables are measured over some occasions in order to study the mean changes of these patients. How we can generate and analyze this type of data for complete and incomplete cases is the main goal of this dissertation. It consists of three main studies about the analysis of multivariate binary longitudinal data. The first study is a method to generate correlated binary data for a multivariate longitudinal model with specified correlation structure. This specified structure allows the correlation to be induced over the outcomes or occasions. Second study is a comparison of three methods for analyzing multivariate binary longitudinal data; each one can be beneficial for determined aims. Also, we investigated the difference among the parameter estimations of the three methods. The third study is an investigation of missing data analysis via GEE models, controlling the correlation over the occasions and outcomes via simulation study. However, several methods for handling missing data are used to reduce the bias of the parameter estimations for the incomplete data. these three studies are presented in separated chapters of this dissertation. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2016. / December 9, 2016. / analysis, binary, correlated, GEE, longitunal, multivariate / Includes bibliographical references. / Elizabeth H. Slate, Professor Directing Dissertation; Amy M. Wetherby, University Representative; Daniel L. McGee, Committee Member; Debajyoti Sinha, Committee Member.

Identifying influential observations in the data is desired to ensure proper inference and statistical analysis. Modern methods to identify influence cases uses cross-validation diagnostics based on the effect of deletion of i-th observation on inference. A popular method to identify influential observations is to use Kullback-Liebler divergence measure between the posterior distribution of the parameter of interest given full data and the posterior distribution given the cross-validated data, where the cross-validated data has the i-th observation removed. Although, in Bayesian inference, the posterior distribution contains all the relevant information about a parameter of interest, when the goal is prediction, perhaps the predictive distribution should be used to identifying influential observations. So, we extended our method to the comparison of the posterior predictive distributions given full data and cross-validated data. We generalize and extend existing popular Bayesian cross-validated influence diagnostics using Bregman divergence based measure (BD). We derive useful properties of these BD based on the influence of each observation on the posterior distribution and we show that it can be extended to the predictive distribution. We show that these BD based measures allow interpretable calibration and that they can be computed via Monte Carlo Markov Chain (MCMC) samples from a single posterior based on full data. We illustrate how our new measure of influence of observations have more useful practical roles for data analysis than popular Bayesian residual analysis tools (CPO) in an example of meta-analysis with binary response and in other cases of interval-censored data. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2018. / July 19, 2018. / Bayesian data analysis, Bregman Divergence, influence measures, Interval-Censored data, Kullback-Liebler, Meta-Analysis / Includes bibliographical references. / Debajyoti Sinha, Professor Directing Dissertation; Lynn Panton, University Representative; Jonathan Bradley, Committee Member; Antonio Linero, Committee Member; Stuart Lipsitz, Committee Member.

No description available.

The theme of this dissertation is to develop robust statistical approaches for the high-dimensional observational data. The development of technology makes data sets more accessible than any other time in history. Abundant data leads to numerous appealing findings and at the same time, requires more thoughtful efforts. We are encountered many obstacles when dealing with high-dimensional data. Heterogeneity and complex interaction structure rule out the traditional mean regression method and expect a novel approach to circumvent the complexity and obtain significant conclusions. Missing data mechanism in high-dimensional data is complicated and is hard to manage with existing methods. This dissertation contains three parts to tackle these obstacles: (1) a tree-based method integrated with the domain knowledge to improve prediction accuracy; (2) a tree-based method with linear splits to accommodate the large-scale and highly correlated data set; (3) an integrative analysis method to reduce the dimension and impute the block-wise missing data simultaneously. In the first part of the dissertation, we propose a tree-based method called conditional quantile random forest (CQRF) to improve the screening and intervention of the onset of mentor disorder incorporating with rich and comprehensive electronic medical records (EMR). Our research is motivated by the REactions to Acute Care and Hospitalization (REACH) study, which is an ongoing prospective observational cohort study of the patient with symptoms of a suspected acute coronary syndrome (ACS). We aim to develop a robust and effective statistical prediction method. The proposed approach fully takes the population heterogeneity into account. We partition the sample space guided by quantile regression over the entire quantile process. The proposed CQRF can provide a more comprehensive and accurate prediction. We also provide theoretical justification for the estimate quantile process. In the second part of the dissertation, we apply the proposed CQRF to REACH data set. The predictive analysis derived by the proposed approach shows that for both entire samples and high-risk group, the proposed CQRF provides more accurate predictions compared with other existing and widely used methods. The variable importance scores give a promising result based on the proposed CQRF that the proposed importance scores identify two variables which have been proved to be critical features by the qualitative study. We also apply the proposed CQRF to Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study data set. We show that the proposed approach improves the personalized medicine recommendation compared with existing treatment recommendation method. We also conduct two simulation studies based on the two real data sets. Both simulation studies validate the consistent property of the estimated quantile process. In the second part, we also extend the proposed CQRF with univariate splits to linear splits to accommodate a large number of highly correlated variables. Gene-environment interaction is a widely concerned topic since the traits of complex disease is always difficult to understand, and we are eager to find interventions tailored to individual genetic variations. The proposed approach is applied to a Breast Cancer Family Registry (BCFR) study data set with body mass index (BMI) as the response variable, several nutrition intake factors, and genotype variables. We aim to figure out what kind of genetic variations affect the heterogeneous effect of the environmental factors on BMI. We devise a criterion which measures the relationship between the response variable and gene variants conditioning on the environmental factor to determine the optimal linear combination split. The variable importance score is also calculated by summing up the criterion across all splits in the random forest. We show in the results that top-ranked genes prioritized by the proposed importance scores make the effect of the environmental factors on BMI differently. In the third part, we introduce an integrative analysis approach called generalized integrative principal component analysis (GIPCA). The heterogeneous data types and the presence of block-wise missing data pose significant challenges to the integration of multi-source data and further statistical analyses. There is not literature can easily accommodate data of multiple types with block-wise missing structure. The proposed GIPCA is a low-rank method which conducts the dimension reduction and imputation of block-wise missing data simultaneously to data with multiple types. Both simulation study and real data analysis show that the proposed approach achieves good missing data imputation accuracy and identifies some meaningful signals.