BASIS OF STATISTICAL INFERENCE

Author: MEIRA MACHADO LUÍS FILIPE.
Year: 2005.
University: SANTIAGO DE COMPOSTELA [www.usc.es].
Place of defense: FACULTADE DE MATEMÁTICAS.
Place of preparation: FACULTADE DE MATEMATICAS.

Summary: The progression of a certain disease can be described by the models multi-estado. These models can be viewed as a generalization of the process of survival where several events (intermediate) occur consecutively in time. In this context, some issues of interest include: the estimated rates progresi6n, evaluacl6n the effects of individual risk factors, or the estimated survival rate. The influence of these events in the intermediate survival is usually analyzed by Cox regression model. This thesis contains a comprehensive review of the models multi-estado more common to study the progression of the disease. We discuss the differences between these models and model regresi6n Cox, emphasizing the potential advantages and disadvantages of each method. The revised methods are illustrated with data from heart transplant at Stanford, providing a gula on using these metodologlas for the study of disease progression. A atenci6n particular should be given when one is interested in assessing the effect of a covariate. The Cox proporciona-estimaciones constant model of the effect of covariable over the period estudio.-Para-evitar this problem utilizan-métodos Ae smoothing spline (P-splines). In addition, these methods are introduced spline modeling multi-estado to ascertain the possible nonlinear effects of covariates in the intensities of transition. The use of these methods in models mutti-estado is novel. To illustrate the potential benefits of using models multi-estado, several studies were conducted simulation. Through these studies, explains why the Cox model may not be appropriate (with hard) when used in the presence of time-dependent covariates. Traditionally, statistical methods to analyze models multi-estado depend on the budget Markov. Under the ownership of Markov, intensid des transition depend on the current time and the state currently occupied but not depend on the patient's history (time spent in the current state; times of transition from one state to another, and so on. ). Ignoring the history of the disease, these models can present serious limitations, Devando then a bad specification. An alternative approach is to use the budget semi-Markov, whereby the future of the process is not dependent on the current time, if not just for the duration in the current state. In this dissertation is revised model Cox semi-Markov and proposes a new approach no-Markoviano, which allows the intensities of transition may depend not only on the current time, but also time transici6n to its current state. Research on models no-Markovianos has two main objectives. The first objective is desarroHar a new approach based on budgets less restrictive than those based on the Markov property. The second objective is to compare the estimators developed aqur for the probability of transition estimates Aalen-Johansen (arising under the budget Markov). One important limitation to the application of models multi-estado is the limited availability of software "friendly" for these models. The majority of the available software presents some challenges and constraints in practice. For all eRo, a program was developed in R lIamado tdc.surv, which can be used to adjust a simple and compact the largest of the models studied. The advantages of this software include the same input data to adjust to the different models, providing the numerical results and graphic co 8 rrespond 33e dent. In this way, users can analyze the results offered through different models, comparar1os between sr and make decisions.