Modelos de sobrevivência induzidos por fragilidade - Sacramento, Michele Maciel (2024)
Applications in survival analysis can incorporate covariates, such as age, sex, disease severity, or laboratory data, which are known. However, there are many other unknown factors that can influence an individual's survival, including health status, lifestyle, smoking, occupation, and genetic risk factors. These factors are referred to as frailty and control the unobserved heterogeneity of the study's individuals. Thus, the objective of this work is to develop frailty models for modeling unobserved heterogeneity in survival data. In this context, the Family of Power Variance Functions (PVF) will be considered for modeling the unobserved heterogeneity of these data and the Piecewise Exponential Model (MEP) will be adopted as the baseline hazard function. The proposed approach is flexible, as the PVF distribution includes major frailty models as special cases and, in turn, the MEP model provides a semiparametric alternative to parametric distributions, being widely used due to its ability to accommodate hazard functions in different forms, without the need to impose restrictions to achieve a good fit to the data. Consequently, the presented models are extended to allow the construction of defective and long-duration univariate models, resulting in zero frailty, where it is possible to determine the proportion of individuals immune to the event of interest in survival studies. Furthermore, a bivariate long-duration frailty model is introduced, using Poisson mixture and the PVF family distributions. This model is enhanced, generating a regression model that allows the assessment of the impact of covariates on survival data. The inferential approach is based on bayesian methods using the Hamiltonian Monte Carlo method implemented in R-Stan, where some simulation results are provided to evaluate the performance of certain properties of the Bayes estimators. The importance of models is illustrated through applications to real data sets.