@PHDTHESIS{ 2024:1577865306,
 	title = {Essays on cure rate models},
 	year = {2024},
 	url = "https://tede.ufam.edu.br/handle/tede/10150",
 	abstract = "In survival analysis, cure fraction models are fundamental in applications where a significant portion of the individuals studied will never experience the event of interest, even if observed over a long period of time. These models implicitly assume that all individuals under study belong to a homogeneous population and include the assumption of the existence of an unobserved random variable, representing information not directly available in the data. This work is divided into three chapters, in which in the first we present an introduction to the cure rate models. In the following chapters we address new methodologies developed in this work in the context of survival analysis models with cure fraction, considering the Weibull distribution for lifetime. In the second chapter our proposal is to extend the cure fraction model with competitive causes in Power Series assuming a mixture of two competitive causes belonging from this class. This mixture includes several well-known models as special cases. The estimation of parameters is discussed using the maximum likelihood method, with the proposition of an EM (Expectation-Maximization) type-algorithm. Monte Carlo studies were conducted to evaluate the asymptotic properties. We illustrate our methodology through an application to a set of medical data from a population study of incident cases of cutaneous melanoma diagnosed in the state of São Paulo, Brazil. In the third chapter, we present a new modeling via cure fraction considering that the number of competing causes for the event of interest follows a mixture of the Poisson and Birnbaum-Saunders distributions. Some statistical properties are presented, especially that the promotion time model appears as a limiting case. Parameter estimation is conducted using the maximum likelihood method, in which an EM (Expectation-Maximization) type-algorithm is proposed for this purpose. Monte Carlo experiment are studied to evaluate the asymptotic properties, as well as a study of the power of likelihood ratio test. An application is discussed using real data from a population study of incident cases of breast cancer in the state of São Paulo, Brazil.",
 	publisher = {Universidade Federal do Amazonas - Universidade do Estado do Pará},
 	scholl = {Programa de Pós-graduação em Matemática},
 	note = {Instituto de Ciências Exatas}
}