Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [127]-129).

Thesis (Ph. D.)--Florida State University, 2005. / Advisor: Dr. Ian W. McKeague, Florida State University, College of Arts and Sciences, Dept. of Statistics. Title and description from dissertation home page (viewed June 16, 2005). Document formatted into pages; contains vii, 73 pages. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xi, 108 p.; also includes graphics (some col.) Includes bibliographical references (p. 101-108). Available online via OhioLINK's ETD Center

In clinical trials, patients are enrolled into two treatment arms. A researcher may be interested in studying the effectiveness of a new drug or the comparison of two drugs for the treatment of a disease. This survival data is later analysed using the logrank test or the Cox regression model to detect differences in survivor functions. However, the power function of the logrank test depends solely on the number of patients enrolled into the study. Because statisticians will always minimise type I and type II errors, a researcher carrying out a clinical trial must define beforehand, the number of patients to be enrolled into the clinical study. Without proper sample size and power estimation a clinical trial may fail to detect a false hypothesis of the equality of survivor functions. This study presents through simulation, a way of power and sample size estimation for clinical trials that use the logrank test for their data analysis and suggests an easy method to estimate power and sample size in such clinical studies. Findings on power analysis and sample size estimation on logrank test are applied to two real examples: one is the Veterans' Administration Lung Cancer study; and the other is the data from a placebo controlled trial of gamma interferon in chronic granulotomous disease.

In sub-Saharan Africa, resource-limitation results in scarce availability of HIV prognostic tools such as CD4+ T-Lymphocyte (CD4) count and HIV viral load. To facilitate counselling and clinical decisions in this setting, widely available and inexpensive markers of prognosis are required. Chapter one gives an overview of the epidemiology and pathophysiology of HIV infection (with particular reference to sub-Saharan Africa), and its clinical manifestations. Staging systems for HIV infection and aspects of management in resource-poor environments are briefly discussed. Chapter two describes the epidemiological, pathophysiological and clinical aspects of tuberculosis (TB) in HIV infected patients, the commonest opportunistic infection in sub-Saharan Africa. It further provides HIV and TB prevalence data from the Western Cape, South Africa. In chapter three a study is presented demonstrating the usefulness of the total lymphocyte count (TLC) in combination with the World Health Organisation (WHO) clinical staging system to predict outcome in 831 HIV positive patients. A TLC of 1250/μL was found to be the equivalent of a CD4 count of 200/μL. Patients with early HIV disease (WHO stage 1&2) had low annual rates of progression to AIDS : 3-4% if the TLC was above 1250/μL, 12-14% if the TLC was below 1250/μL. Annual progression to AIDS increased to 25% and 46% in patients with clinical stage 3 and a TLC above or below 1250/μL respectively. Patients with AIDS had 30-55% one-year mortality rates depending on the TLC. Chapter four illustrates that pulmonary tuberculosis (PTB) in HIV infected patients presents with a radiographic spectrum reflecting the degree of HIV induced immune suppression. Chest radiographs and pre-treatment total lymphocyte counts provide prognostic information. Upper zone cavitatory infiltrates typical of reactivation PTB were associated with a preserved CD4 count (mean 389/μL) and predicted a 100% two-year survival. Pleural effusions were associated with a mean CD4 count of 184/μL and predicted 65% two-year survival. Patients with atypical radiographic presentation, including lower and mid-zone infiltrates, hilar and mediastinal adenopathy or interstitial patterns, had low CD4 counts (mean 105/μL) and a 36% survival at two years. Rather than classifying every patient with pleura-pulmonary tuberculosis as WHO stage 3, incorporation of the prognostic value of the chest radiograph into the clinical staging system, such that typical reactivation PTB becomes stage 2, tuberculous pleural effusion stage 3 and atypical PTB stage 4, would enhance the prognostic accuracy of HIV related tuberculosis. Chapter five demonstrates that patients with AIDS could be categorized accord ing to one of three survival patterns, relating to the type of opportunistic illness. One-year survival rates were highest for extra-pulmonary tuberculosis and herpes simplex virus infection (70% ); intermediate for oesophageal candidiasis, cryptococcal meningitis, kaposi sarcoma and pneumocystis carinii pneumonia (45%) ; and poorest for the HIV wasting syndrome, AIDS-dementia complex and performance status 4 (20%). Despite the overall poor prognosis associated with the acquired immunodeficiency syndrome, a substantial proportion of patients survive, even in the absence of anti-retroviral therapy, for a number of years. Chapter six concludes by proposing how the data presented in this thesis could be used in the clinical management of patients with HIV infection in a resource limited environment.

Survival data was obtained from a regional dialysis clinic. The data was divided into two groups, diabetic and non-diabetic. This data was compared to see if the survival rates of the two groups differed significantly. They were compared using the life-table, Kaplan-Meier and proportional hazards methods. Also a parametric comparison based on the Weibull distribution, was performed. The data of the diabetic patients was further split into adult-onset and juvenile-onset diabetes. These groups were compared using the three non-parametric methods and were found not to be significantly different. Thus the two types of diabetics could be treated as one group when comparing diabetics and non-diabetics. It was found that the non-diabetics had a significantly higher survival rate than the diabetics. The cofactors that were found to influence survival in an adverse way were the presence of diabetes and the age at initial dialysis. / Thesis / Master of Science (MSc)

published_or_final_version / Statistics / Master / Master of Philosophy

Because of the measuring instrument or the biological variability, many studies with survival data involve covariates which are subject to measurement error. In such cases, the naive estimates are usually biased. In this thesis, we propose a bias corrected estimate of the regression parameter for the multinomial probit regression model with covariate measurement error. Our method handles the case when the response variable is subject to interval censoring, a frequent occurrence in many medical and health studies where patients are followed periodically. A sandwich estimator for the variance is also proposed. Our procedure can be generalized to general measurement error distribution as long as the first four moments of the measurement error are known. The results of extensive simulations show that our approach is very effective in eliminating the bias when the measurement error is not too large relative to the error term of the regression model. / Censoring is an intrinsic part in survival analysis. In this thesis, we establish the asymptotic properties of MMLE to general transformation models when data is subject to right or left censoring. We show that MMLE is not only consistent and asymptotically normal, but also asymptotically efficient. Thus our asymptotic results give a definite answer to a long-term argument on the efficiency of the maximum marginal likelihood estimator. The difficulty in establishing these results comes from the fact that the score function derived from the marginal likelihood does not have ordinary independence or martingale structure. We will develop a discretization method in establishing our results. As a special case, our results imply the consistency, asymptotic normality and efficiency for the multinomial probit regression, a popular alternative to the Cox regression model. / General transformation model is an important family of semiparametric models in survival analysis which generalizes the linear transformation model. It not only includes typical Cox regression model, proportional odds model and multinomial probit regression model, but also includes heteroscedastic hazard regression model, general heteroscedastic rank regression model and frailty model. By maximizing the marginal likelihood, a parameter estimation (MMLE) can be obtained with the property that it avoids estimating the baseline survival function and censoring distribution, and such property is enjoyed by the Cox regression model. In this thesis, we study three areas of generalization of general transformation models: main response variable is subject to censoring, covariates are time-varying and covariates are subject to measurement error. / In medical studies, the covariates are not always the same during the whole period of study. Covariates may change at certain time points. For example, at the beginning, n patients accept drug A as treatment. After certain percentage of patients have died, the investigator might add new drug B to the rest of the patients. This corresponds to the case of time-varying covariates. In this thesis, we propose an estimation procedure for the parameters in general transformation model with this type of time-varying covariates. The results of extensive simulations show that our approach works well. / Wu, Yueqin. / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3589. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 74-78). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Tsui Yuen-Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 53-56). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Parametric Regressions in Survival Analysis --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Exponential Regression --- p.7 / Chapter 2.3 --- Weibull Regression --- p.8 / Chapter 2.4 --- Maximum Likelihood Method --- p.9 / Chapter 2.5 --- Diagnostic --- p.10 / Chapter 3 --- Local Influence --- p.13 / Chapter 3.1 --- Introduction --- p.13 / Chapter 3.2 --- Development --- p.14 / Chapter 3.2.1 --- Normal Curvature --- p.14 / Chapter 3.2.2 --- Conformal Normal Curvature --- p.15 / Chapter 3.2.3 --- Q-displacement Function --- p.16 / Chapter 3.3 --- Perturbation Scheme --- p.17 / Chapter 4 --- Examples --- p.21 / Chapter 4.1 --- Halibut Data --- p.21 / Chapter 4.1.1 --- The Data --- p.22 / Chapter 4.1.2 --- Initial Analysis --- p.23 / Chapter 4.1.3 --- Perturbations of σ around 1 --- p.23 / Chapter 4.2 --- Diabetic Data --- p.30 / Chapter 4.2.1 --- The Data --- p.30 / Chapter 4.2.2 --- Initial Anaylsis --- p.31 / Chapter 4.2.3 --- Perturbations of σ around σ --- p.31 / Chapter 5 --- Conclusion Remarks and Further Research Topic --- p.35 / Appendix A --- p.38 / Appendix B --- p.47 / Bibliography --- p.53

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy