Modelos com fragilidade em analise de sobrevivencia.

The aim of this thesis is the study of probabilistic survival models for heterogeneous populations, with special emphasis on frailty models. Whenever heterogeneity can be totally explained in terms of observable co variates, regression models are appropriate. Here, we investigate the consistency of Aalen linear regression model (1989, 1992), when co variates are omitted. Nowadays, there is an increasing concern about the impact of unobserved heterogeneity due, for instance, to the fact that it may not have been possible to record all relevant risk factors. The necessity of taking into account such heterogeneity has led to the development of frailty models. Considering the multiplicative model introduced by Vaupel et al. (1979), we propose a new family of distributions derived from the Pareto distribution. Its properties show that these distributions are relevant for application as frailty distributions. Next, we introduce an alternative model, where frailty acts additively on the hazard function. This additive model can have a competing risks interpretation. Also, we present the results obtained when the frailty distribution belongs to a non-negative exponential family. Finally, we propose the non central chi squared distribution with zero degrees of freedom as a frailty distribution with zero degrees of freedom as a frailty distribution, in the case where heterogeneity is due to the existence, in the population, of some individuals which are non-susceptible to the event of interest.Available from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1249-074 Lisboa, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga