First, we present two novel semiparametric survival models with log-linear median regression functions for right censored survival data. These models are useful alternatives to the popular Cox (1972) model and linear transformation models (Cheng et al., 1995). Compared to existing semiparametric models, our models have many important practical advantages, including interpretation of the regression parameters via the median and the ability to address heteroscedasticity. We demonstrate that our modeling techniques facilitate the ease of prior elicitation and computation for both parametric and semiparametric Bayesian analysis of survival data. We illustrate the advantages of our modeling, as well as model diagnostics, via reanalysis of a small-cell lung cancer study. Results of our simulation study provide further guidance regarding appropriate modelling in practice. Our second goal is to develop the methods of analysis and associated theoretical properties for interval censored and current status survival data. These new regression models use log-linear regression function for the median. We present frequentist and Bayesian procedures for estimation of the regression parameters. Our model is a useful and practical alternative to the popular semiparametric models which focus on modeling the hazard function. We illustrate the advantages and properties of our proposed methods via reanalyzing a breast cancer study. Our other aim is to develop a model which is able to account for the heteroscedasticity of response, together with robust parameter estimation and outlier detection using sparsity penalization. Some preliminary simulation studies have been conducted to compare the performance of proposed model and existing median lasso regression model. Considering the estimation bias, mean squared error and other identication benchmark measures, our proposed model performs better than the competing frequentist estimator. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2012. / March 26, 2012. / Bayesian Analysis, Median regression, Semiparametric, Survival Analysis, Transform-Both-Sides / Includes bibliographical references. / Debajyoti Sinha, Professor Directing Thesis; Yi Zhou, University Representative; Stuart Lipsitz, Committee Member; Dan McGee, Committee Member; Xu-Feng Niu, Committee Member; Yiyuan She, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_182976 |
| Contributors | Lin, Jianchang, 1983- (authoraut), Sinha, Debajyoti (professor directing thesis), Zhou, Yi (university representative), Lipsitz, Stuart (committee member), McGee, Dan (committee member), Niu, Xu-Feng (committee member), She, Yiyuan (committee member), Department of Statistics (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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