Master of Science / Department of Statistics / James J. Higgins / The time for an event to take place in an individual is called a survival time. Examples include the time that an individual survives after being diagnosed with a terminal illness or the time that an electronic component functions before failing. A popular parametric model for this type of data is the Weibull model, which is a flexible model that allows for the inclusion of covariates of the survival times. If distributional assumptions are not met or cannot be verified, researchers may turn to the semi-parametric Cox proportional hazards model. This model also allows for the inclusion of covariates of survival times but with less restrictive assumptions. This report compares estimates of the slope of the covariate in the proportional hazards model using the parametric Weibull model and the semi-parametric Cox proportional hazards model to estimate the slope. Properties of these models are discussed in Chapter 1. Numerical examples and a comparison of the mean square errors of the estimates of the slope of the covariate for various sample sizes and for uncensored and censored data are discussed in Chapter 2. When the shape parameter is known, the Weibull model far out performs the Cox proportional hazards model, but when the shape parameter is unknown, the Cox proportional hazards model and the Weibull model give comparable results.

The objective of the present study is to investigate key aspects of ovarian and breast cancers, which are two main causes of mortality among women. Identification of the true behavior of survivorship and influential risk factors is essential in designing treatment protocols, increasing disease awareness and preventing possible causes of disease. There is a commonly held belief that African Americans have a higher risk of cancer mortality. We studied racial disparities of women diagnosed with ovarian cancer on overall and disease-free survival and found out that there is no significant difference in the survival experience among the three races: Whites, African Americans and Other races. Tumor sizes at diagnosis among the races were significantly different, as African American women tend to have larger ovarian tumor sizes at the diagnosis. Prognostic models play a major role in health data research. They can be used to estimate adjusted survival probabilities and absolute and relative risks, and to determine significantly contributing risk factors. A prognostic model will be a valuable tool only if it is developed carefully, evaluating the underlying model assumptions and inadequacies and determining if the most relevant model to address the study objectives is selected. In the present study we developed such statistical models for survival data of ovarian and breast cancers. We found that the histology of ovarian cancer had risk ratios that vary over time. We built two types of parametric models to estimate absolute risks and survival probabilities and to adjust the time dependency of the relative risk of Histology. One parametric model is based on classical probability distributions and the other is a more flexible parametric model that estimates the baseline cumulative hazard function using spline functions. In contrast to women diagnosed with ovarian cancer, women with breast cancer showed significantly different survivorship among races where Whites had a poorer overall survival rate compared to African Americans and Other races. In the breast cancer study, we identified that age and progesterone receptor status have time dependent hazard ratios and age and tumor size display non-linear effects on the hazard. We adjusted those non-proportional hazards and non-linear effects by using an extended Cox regression model in order to generate more meaningful interpretations of the data.

The main goal of this study is to seek the effects of some risk and prognostic factors contributing to survival of female invasive breast cancer in United States. The study presents the survival analysis for the adult female invasive breast cancer based on the datasets chosen from the Surveillance Epidemiology and End Results (SEER) program of National Cancer Institute (NCI). In this study, the Cox proportional hazard regression model and logistic regression model were employed for statistical analysis. The odds ratios (OR), hazard ratios (HR) and confidence interval (C.I.) were obtained for the risk and prognosis factors. The study results showed that some risk and prognosis factors, such as the demographic factors (race and age), social and family factor (marital status), biomedical factors (tumor size, disease stage, tumor markers and tumor cell differentiation level etc.) and type of treatment patients received had significant effects on survival of the female invasive breast cancer patients.

A truncated sample consists of realizations of a pair of random variables (L, T) subject to the constraint that L ≤T. The major study interest with a truncated sample is to find the marginal distributions of L and T. Many studies have been done with the assumption that L and T are independent. We introduce a new way to specify a Cox model for a truncated sample, assuming that the truncation time is a predictor of T, and this causes the dependence between L and T. We develop an algorithm to obtain the adjusted risk sets and use the Kaplan-Meier estimator to estimate the Marginal distribution of L. We further extend our method to more practical situation, in which the Cox model includes other covariates associated with T. Simulation studies have been conducted to investigate the performances of the Cox model and the new estimators.

Many statistical methods for truncated data rely on the assumption that the failure and truncation time are independent, which can be unrealistic in applications. The study cohorts obtained from bone marrow transplant (BMT) registry data are commonly recognized as truncated samples, the time-to-failure is truncated by the transplant time. There are clinical evidences that a longer transplant waiting time is a worse prognosis of survivorship. Therefore, it is reasonable to assume the dependence between transplant and failure time. To better analyze BMT registry data, we utilize a Cox analysis in which the transplant time is both a truncation variable and a predictor of the time-to-failure. An inverse-probability-weighted (IPW) estimator is proposed to estimate the distribution of transplant time. Usefulness of the IPW approach is demonstrated through a simulation study and a real application.

No description available.

The main aim of this study is to explore the effects of risk factors contributing to death in the elderly American population. To achieve this purpose, we constructed Cox proportional hazard regression models and logistic regression models with the complex survey dataset from the national Second Longitudinal Study of Aging (LSOA II) to calculate the hazard ratios (HR)/odds ratios (OR) and confidence interval (CI) of risk factors. Our results show that in addition to chronic disease conditions, many risk factors, such as demographic factors (gender and age), social factors (interaction with friends or relatives), personal health behaviors (smoking and exercise), and biomedical factors (Body mass index and emotional factors) have significant effects on death in the elderly American population. This will provide important information for elderly people to prolong lifespan regardless of whether they have chronic disease/diseases or not.

Submitted by (ana.araujo@ufrpe.br) on 2016-06-28T13:38:54Z No. of bitstreams: 1 Damocles Aurelio Nascimento da Silva.pdf: 694209 bytes, checksum: 1f6f75597b9348c94d982a8d8a612c8e (MD5) / Made available in DSpace on 2016-06-28T13:38:54Z (GMT). No. of bitstreams: 1 Damocles Aurelio Nascimento da Silva.pdf: 694209 bytes, checksum: 1f6f75597b9348c94d982a8d8a612c8e (MD5) Previous issue date: 2006-02-24 / Aiming at to contribute, as alternative to minimize the resources of impacts,mainly, for the search of combustible material to take care of the energy demand of the Brazilian half-barren region, we use the techniques of analysis of survival for understanding of a forest of eucalyptus to the long one of the time, and with this to ration the use wooden as combustible for ceramics, bakeries and existing calcinatory of plaster in region. The data given proceeding from a transversal study of 1500 cells of eucalyptus, divided in 4 stratus, taking as base the period of 03/2002 to 09/2004. The graph of probability was used initially for, being based on the test of Anderson-Darling, takes the decision of which function of probability would use in such a way in the classic study as in the Bayesian boarding. A time taken to the decision of choice of the probability distribution, we use the method of Kaplan-Meier and the Actuarial method (life table) to determine the estimates of the parameters and the test distribution free log-rank to test if the curves of the function of probability differed between categories from one same one variable. We used this test to the level of significance of 5%. For these analyses, it was used statistical software Minitab 13 version and statistical package SAS.In the Bayesian boarding was used method Carlo the Mount Chain of Markov (MCMC) for estimate of parameters, using as priori the distribution gamma,found in literature as the distribution that more good was adjusted for biological data and as function of density, used it of the Weibull distribution, chosen as of the better adjustment to the data according to test of Anderson-darling. For thisanalysis software Winbugs 1.4 was used. The results how much to the analysis of the parameters they had indicated that the joined estimates had been closed, same using distinct methods of estimation. As much was concluded that the best distribution to analyze the population in question is the Weibull, according to test of Anderson-Darling and as method for estimation of the parameters of the distribution, the classic method,how much the Bayesian method, reveals good estimators, verified for the amplitude of the intervals reliable 95%. In face of the results, we conclude that if it must have one better control of the eucalyptus, in first the six months of the plantation. / Visando contribuir, como alternativa para minimizar os impactos antrópicos de caracter negativo causado, principalmente, pela busca de material combustível para atender a demanda energética da região semi-árida brasileira, utilizamos as técnicas de análise de sobrevivência para compreensão do comportamento de uma floresta de eucaliptos ao longo do tempo, e com isto racionar o uso de madeira como combustível por cerâmicas, padarias, casas de farinha e calcinadoras de gesso existentes na região. Usaremos dados provenientes de um estudo transversal de 1500 células de eucaliptos, dividido em 4 estratos, tomando como base o período de 03/2002 a 09/2004.Utilizou-se inicialmente o gráfico de probabilidade para, baseado no teste de Anderson-Darling, tomarmos a decisão de qual função de probabilidade utilizaríamos tanto no estudo clássico como na abordagem bayesiana. Uma vez tomada a decisão de escolha da distribuição de probabilidade, utilizamos o método de Kaplan-Meier e o método Atuarial (tábua de vida) para estimativa dos parâmetros e o teste não paramétrico log-rank para testar se as curvas da função de probabilidade diferiam entre categorias de uma mesma variável. Utilizamos esse teste ao nível de significância de 0,05. Para essas análises, foi utilizado o software estatístico Minitab versão 13 e o pacote estatístico SAS.Na abordagem bayesiana utilizou-se a o método de Monte Carlo Cadeia de Markov (MCMC) para estimativa dos parâmetros, utilizando como priori a distribuição gamma, encontrada na literatura como a distribuição que melhor adequa-se para dados biológicos e como função de densidade, utilizou-se a da distribuição Weibull, escolhida como a de melhor ajuste as dados segundo o teste de Anderson-Darling. Para essa análise foi utilizado o Winbugs 1.4.Os resultados quanto a análise dos parâmetros indicaram que as estimativas encontradas foram próxima, mesmo utilizando métodos de estimação distintos. Conclui-se que a melhor distribuição para analisar a população em questão é a Weibull, segundo o teste de Anderson-Darling e como método para estimação dos parâmetros da distribuição, tanto o método clássico, quanto o método bayesiano, mostram-se bons estimadores, verificado pela amplitude dos intervalos de confiança a 95%. Em face dos resultados, concluímos que deve-seter um melhor controle dos eucaliptos, nos primeiros 6 meses de plantio.

O modelo semiparamétrico de Cox é frequentemente utilizado na modelagem de dados de sobrevivência, pois é um modelo muito flexível e permite avaliar o efeito das covariáveis sobre a taxa de falha. Uma das principais vantagens é a fácil interpretação, de modo que a razão de riscos de dois indivíduos não varia ao longo do tempo. No entanto, em algumas situações a proporcionalidade dos riscos para uma dada covariável pode não ser válida e, este caso, uma abordagem que não dependa de tal suposição é necessária. Nesta tese, propomos um modelo tipo Cox em que o efeito da covariável e a função de risco basal são representadas via bases de Fourier e ondaletas de Haar clássicas e deformadas. Propomos também um procedimento de predição da função de sobrevivência para um paciente específico. Estudos de simulações e aplicações a dados reais sugerem que nosso método pode ser uma ferramenta valiosa em situações práticas em que o efeito da covariável é dependente do tempo. Por meio destes estudos, fazemos comparações entre as duas abordagens propostas, e comparações com outra já conhecida na literatura, onde verificamos resultados satisfatórios. / The semiparametric Cox model is often considered when modeling survival data. It is very flexible, allowing for the evaluation of covariates effects. One of its main advantages is the easy of interpretation, as long as the rate of the hazards for two individuals does not vary over time. However, this proportionality of the hazards may not be true in some practical situations and, in this case, an approach not relying on such assumption is needed. In this thesis we propose a Cox-type model that allows for time-varying covariate effects, for which the baseline hazard is based on Fourier series and wavelets on a time-frequency representation. We derive a prediction method for the survival of future patients with any specific set of covariates. Simulations and an application to a real data set suggest that our method may be a valuable tool to model data in practical situations where covariate effects vary over time. Through these studies, we make comparisons between the two approaches proposed here and comparisons with other already known in the literature, where we verify satisfactory results.

O modelo semiparamétrico de Cox é frequentemente utilizado na modelagem de dados de sobrevivência, pois é um modelo muito flexível e permite avaliar o efeito das covariáveis sobre a taxa de falha. Uma das principais vantagens é a fácil interpretação, de modo que a razão de riscos de dois indivíduos não varia ao longo do tempo. No entanto, em algumas situações a proporcionalidade dos riscos para uma dada covariável pode não ser válida e, este caso, uma abordagem que não dependa de tal suposição é necessária. Nesta tese, propomos um modelo tipo Cox em que o efeito da covariável e a função de risco basal são representadas via bases de Fourier e ondaletas de Haar clássicas e deformadas. Propomos também um procedimento de predição da função de sobrevivência para um paciente específico. Estudos de simulações e aplicações a dados reais sugerem que nosso método pode ser uma ferramenta valiosa em situações práticas em que o efeito da covariável é dependente do tempo. Por meio destes estudos, fazemos comparações entre as duas abordagens propostas, e comparações com outra já conhecida na literatura, onde verificamos resultados satisfatórios. / The semiparametric Cox model is often considered when modeling survival data. It is very flexible, allowing for the evaluation of covariates effects. One of its main advantages is the easy of interpretation, as long as the rate of the hazards for two individuals does not vary over time. However, this proportionality of the hazards may not be true in some practical situations and, in this case, an approach not relying on such assumption is needed. In this thesis we propose a Cox-type model that allows for time-varying covariate effects, for which the baseline hazard is based on Fourier series and wavelets on a time-frequency representation. We derive a prediction method for the survival of future patients with any specific set of covariates. Simulations and an application to a real data set suggest that our method may be a valuable tool to model data in practical situations where covariate effects vary over time. Through these studies, we make comparisons between the two approaches proposed here and comparisons with other already known in the literature, where we verify satisfactory results.