Physical Sciences and Mathematics Commons^™

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. …

Parametric Reversed Hazards Model For Left Censored Data With Application To Hiv, Farahnaz Islam

Theses and Dissertations

Left censoring is generally a rare type of censoring in time-to-event data, however there are some fields such as HIV related studies where it commonly occurs. Currently, there is no clear recommendation in the literature on the optimal model and distribution to analyze left-censored data. Recommendations can help researchers apply more accurate models for this type of censoring. This study derives the Parametric Reversed Hazards (PRH) Model for a variety of distributions which may be appropriate for left censored data. The performance of these derived PRH models to analyze HIV viral load data are compared using extensive simulations and a …

Score Test Derivations And Implementations For Bivariate Probability Mass And Density Functions With An Application To Copula Functions, Roy Bower

Theses and Dissertations

This dissertation is comprised and grounded in statistical theory with an application to solving real world problems. In particular, the development and implementation of multiple score tests under a variety of scenarios are derived, applied, and interpreted. In chapter 2, I propose a score test for independence of the marginals based on Lakshminarayana’s bivariate Poisson distribution. Each marginal distribution of the bivariate model is a univariate Poisson distribution, and the parameters of the bivariate distribution can be estimated using maximum likelihood methods. The simulation study shows that the score test maintains size close to the nominal level. To assess the …