Novas modelagens de risco aditivo com fragilidade para análise de dados de sobrevivência

Abstract

Survival analysis emerges as a valuable statistical area for examining the time until the occurrence of events of interest. Several models were designed and applied in different areas such as: Medicine, Engineering, Biomedicine and Social Sciences. The model proposed by Cox (1972) stands out as one of the most recognized and used in the analysis of survival data. However, it is important to note that this model assumes that risks are proportional, an assumption that is not always reasonable. An alternative model to Cox proportional hazards models is the additive hazard model that was initially proposed by Aalen (1980). In the additive model, the effect of the covariates is inserted additively into the base hazard function. In many situations there are factors not observed in the study that influence survival time, so for univariate survival data a random effect, called Aalen (1978) and Clayton (1978) as a frailty term, can be entered additively or multiplicatively to estimate this unobserved heterogeneity. In this context, the additively inserted frailty term for risk modeling in univariate data analysis and recurring event data was studied and applied to real data. Furthermore, a proposal for an estimator for individual frailties was presented. Also a cure fraction model with additive frailty was proposed and applied to real data, where this model is applicable to studies in which there are individuals who are considered immune, cured or not susceptible to the event of interest. A new alternative additive risk modeling was also proposed based on Gupta (2016). The maximum likelihood estimation approach was used to estimate the parameters of the models studied, and studies via Monte Carlo simulation were developed to evaluate the behavior of maximum likelihood estimators.