Modelo log-normal com fração de cura no contexto da regressão distribucional

Abstract

Cancer remains one of the leading causes of morbidity and mortality worldwide, exerting a subs- tantial impact on public health and on the quality of life of affected patients. Survival analysis constitutes a fundamental tool for investigating the time until the occurrence of specific events, such as death or disease progression, and plays a pivotal role in cancer research, particularly when dealing with censored data and the presence of a cure fraction. Traditionally, probabilis- tic models such as the Weibull and log-normal distributions have been employed to represent such data. Nevertheless, more flexible approaches, such as generalized additive models for location, scale, and shape (GAMLSS), provide enhanced modeling capabilities, especially in scenarios where data exhibit complex features that are not adequately captured by conventional models. In this context, the present dissertation proposes the use of the log-normal cure model within the GAMLSS framework. The mathematical formalization of the model, its implemen- tation in the gamlss package of the R software, and its application to pancreatic cancer data are presented. The results indicate that the implementation of the log-normal distribution with a cure fraction in the GAMLSS context is well-suited to the data, demonstrating the effective- ness of the proposed methodology in capturing the specific survival dynamics of this disease. Moreover, the model enables the incorporation of covariates that simultaneously explain me- dian survival, variability in survival times, and the probability of cure, thereby underscoring its potential to advance survival analysis in both clinical and epidemiological research settings.