Inaugural-Diss. / Tübingen, Eberhard-Karls-Universität ; 1991.

Este trabalho visa estudar o modelo de Cox-Aalen, que incorpora efeitos fixos e variantes no tempo por meio das estruturas aditiva e multiplicativa. Os principais modelos aditivos e multiplicativos que englobam efeitos fixos e variantes no tempo são revisados com enfoque de processos de contagem e um teste do tipo escore para auxiliar na escolha entre a estrutura aditiva e multiplicativa é proposto e avaliado por meio de estudos de simulação. Aplicação e comparação dos principais modelos discutidos em dados do Instituto do Câncer do Estado de São Paulo (ICESP) sugerem que o modelo estudado pode ser uma opção interessante na análise de dados de sobrevivência em que as ferramentas usuais não são adequadas. / This dissertation aims to study the Cox-Aalen regression model, which incorporates fixed and time-varying effects through the additive and multiplicative structures. The primary additive and multiplicative risk models that deal with fixed and time-dependent effects are reviewed with the counting process framework and a score test to assist the decision between the additive and multiplicative structures is proposed and evaluated with a simulation study. The application of the models to the Instituto do Câncer do Estado de São Paulo (ICESP) dataset suggests that the model under study can be considered as an interesting option to analyse survival data when the usual techniques are not aproppriate.

Este trabalho visa estudar o modelo de Cox-Aalen, que incorpora efeitos fixos e variantes no tempo por meio das estruturas aditiva e multiplicativa. Os principais modelos aditivos e multiplicativos que englobam efeitos fixos e variantes no tempo são revisados com enfoque de processos de contagem e um teste do tipo escore para auxiliar na escolha entre a estrutura aditiva e multiplicativa é proposto e avaliado por meio de estudos de simulação. Aplicação e comparação dos principais modelos discutidos em dados do Instituto do Câncer do Estado de São Paulo (ICESP) sugerem que o modelo estudado pode ser uma opção interessante na análise de dados de sobrevivência em que as ferramentas usuais não são adequadas. / This dissertation aims to study the Cox-Aalen regression model, which incorporates fixed and time-varying effects through the additive and multiplicative structures. The primary additive and multiplicative risk models that deal with fixed and time-dependent effects are reviewed with the counting process framework and a score test to assist the decision between the additive and multiplicative structures is proposed and evaluated with a simulation study. The application of the models to the Instituto do Câncer do Estado de São Paulo (ICESP) dataset suggests that the model under study can be considered as an interesting option to analyse survival data when the usual techniques are not aproppriate.

In this paper, we estimate the parameters $S_0(t)$ and $ eta$ in Cox proportional hazard model when data are all interval-censored. For the application of this model, data should be either exact or right-censored, therefore we transform interval-censored data into exact data by three di®erent methods and then apply Nelson-Aalen estimate to obtain $S_0(t)$ and $ eta$. The test statistic $hat{ eta}^2I(hat{ eta})$ is not approximately distributed as $chi^2_{(1)}$ but $chi^2_{(1)}$ times a constant c.

This work is devoted to seeking methods for analysis of survival data with the Aalen model under special circumstances. We supposed, that all regression functions and all covariates of the observed individuals were nonnegative and we named this class of models monotone Aalen models. To find estimators of the unknown regres- sion functions we considered three maximum likelihood based approaches, namely the nonparametric maximum likelihood method, the Bayesian analysis using Beta processes as the priors for the unknown cumulative regression functions and the Bayesian analysis using a correlated prior approach, where the regression functions were supposed to be jump processes with a martingale structure.

In reliability studies, the goal is to gain knowledge about a product's failure times or life expectancy. Precedence tests do not require large sample sizes and are used in reliability studies to compare the life-time distributions from two samples. Precedence tests are useful since they provide reliable results early in a life-test and the surviving units can be used in other tests. Ng and Balakrishnan (2010) proposed a precedence-type test based on the Kaplan-Meier estimator of the cumulative distribution function. A precedence-type test based on the Nelson-Aalen estimator of the cumulative hazard function has been proposed. This test was developed for both Type-II right censoring and progressive Type-II right censoring. Numerical results, including illustrative examples, critical values and a power study have been provided. The results from this test were compared with those from the test based on the Kaplan-Meier estimator.

In reliability studies, the goal is to gain knowledge about a product's failure times or life expectancy. Precedence tests do not require large sample sizes and are used in reliability studies to compare the life-time distributions from two samples. Precedence tests are useful since they provide reliable results early in a life-test and the surviving units can be used in other tests. Ng and Balakrishnan (2010) proposed a precedence-type test based on the Kaplan-Meier estimator of the cumulative distribution function. A precedence-type test based on the Nelson-Aalen estimator of the cumulative hazard function has been proposed. This test was developed for both Type-II right censoring and progressive Type-II right censoring. Numerical results, including illustrative examples, critical values and a power study have been provided. The results from this test were compared with those from the test based on the Kaplan-Meier estimator.