Modelagem de dados de sobrevivência induzida por fragilidade discreta via versão hurdle da distribuição série de potência zero-modificada

Abstract

Modeling unobserved heterogeneity in survival analysis traditionally relies on frailty models. However, their conventional architecture, based on continuous distributions, is often restrictive in contexts exhibiting a structural cure fraction. To address this limitation, this thesis proposes an innovative discrete frailty model based on the Hurdle Zero-Modified Generalized Poisson (HZMGP) distribution. The proposed model is distinguished by a multifaceted architecture that provides three key advantages: its discrete nature offers a natural representation of cured individuals (zero frailty); its zero-modification structure flexibly accommodates diverse patterns of zeros (inflated, deflated, or truncated); and its inclusion of a dispersion parameter captures variability arising from latent risk factors. Inference for the model was developed and validated under both frequentist and Bayesian paradigms. Extensive simulation studies in both frameworks confirmed the estimators' asymptotic properties and, crucially, demonstrated the model's flexibility to accurately capture scenarios both with and without a cure fraction. The model's utility and versatility are ultimately demonstrated through its application to two contrasting oncology datasets, validating its relevance for clinical practice. Furthermore, the Bayesian framework yielded two of the thesis's most significant contributions: a probabilistic classification rule for individual prognostic stratification, and a novel conceptual interpretation of the dispersion parameter as a statistical proxy for unobserved biological heterogeneity. These advances represent a significant contribution to the analysis of complex survival data.