Physical Sciences and Mathematics Commons^™

Novel Methods For Analyzing Longitudinal Data With Measurement Error In The Time Variable, Caroline Munindi Mulatya

Theses and Dissertations

In some longitudinal studies, the observed time points are often confounded with measurement error due to the sampling conditions, resulting into data with measurement error in the time variable. This type of data occurs mainly in observational studies when the onset of a longitudinal process is unknown or in clinical trials when individual visits do not take place as specified by the study protocol, but are often rounded to coincide with the study protocol. Methodological and inferential implications of error in time varying covariates for both linear and nonlinear models have been studied widely. In this dissertation, we shift attention …

Semiparametric Estimation Methods For Complex Accelerated Failure Time Model, Yinding Wang

Theses and Dissertations

The proportional hazards (PH) model and the accelerated failure time (AFT) model are the two most popular survival models in fitting the right-censored data. The AFT model is a useful alternative to the PH model, particularly when the PH assumption is not satisfied. Usually, the linear association is assumed with logarithm of survival time in the AFT model. However, the nonlinear association may exist in practice. The first project aims to handle the nonlinear component in the AFT model, which is called the semiparametric additive partial accelerated failure time (AP-AFT) model. Two estimation methods based on the rank-smooth method and …

The Reflected-Shifted-Truncated-Gamma Distribution For Negatively Skewed Survival Data With Application To Pediatric Nephrotic Syndrome, Sophia D. Waymyers

Theses and Dissertations

Negatively skewed survival data arise occasionally in public health fields and in statistical research. Standard distributions such as the exponential, generalized F, generalized gamma, Gompertz, log-logistic, lognormal, Rayleigh, and Weibull distributions are not always well suited to this data. The primary goal of this dissertation is to find a viable alternative for modeling negatively skewed survival data such as the time to first remission for pediatric patients with frequently relapsing or steroid dependent nephrotic syndrome.

We begin with a brief introduction of survival analysis and the nature of pediatric nephrotic syndrome. A meta-analysis on atopy and pediatric nephrotic syndrome using …

Sample Size Calculation For Ph Mixture Cure Model, Yihong Zhan

Theses and Dissertations

With the development of advanced medical technology, a significant proportion of patients can be cured of many chronic diseases. Because a substantial fraction of patients have censored information, the standard survival model, such as the proportional hazards (PH) model cannot capture the cured information of patients. Thus PH mixture cure model is developed to handle the survival data with potential cured information. A corresponding sample size formula based on log rank test has been proposed by Wang et al. (2012) and the probability of death in their formula is only contributed by the control arm. However, to calculate the sample …

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 …

Regression Models For Count Data Based On The Double Poisson Distribution, Rebecca Wardrop

Theses and Dissertations

This paper explores the double Poisson distribution. The probability mass function and the difficulties associated with derivative-based optimization for this distribution are discussed. Stata software developed for estimation of double Poisson regression is detailed. Simulations are used to test the software. Data which are over-, under-, and equidispersed relative to the Poisson are generated and the software is utilized to estimate a regression model, a zero-inflated model, and a marginalized zero-inflated model all based on the double Poisson distribution. The estimated power of the test for φ = 1 for the double Poisson models are compared to the power of …

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 …

Spatio-Temporal Analysis Of The Occupational Fatal Victimization Of Law Enforcement Officers In The Us, Xueyi Xing

Theses and Dissertations

The models with constant coefficients of the covariates across space and time are commonly used in spatio-temporal analyses. However, the associations between risk factors and the outcome could have locally differential temporal trends in many cases. In this study, a Bayesian latent cluster modeling strategy is employed to identify potential spatial clusters in which locally specific sets of temporally varying coefficients of covariates are allowed. A state-level panel data of police officers occupational fatal victimization for the years 1979-2010 is used. To accommodate overdisperson and excess zeros, a negative binomial model and zero-inflated Poisson/negative binomial models are also utilized. A …