A família estendida logística generalizada dependente do tempo - GTDEL.

Abstract

Studies have shown that certain survival datasets are not adequately represented by the proportional hazards model proposed by Cox (1972), highlighting the need for alternative approaches that accommodate non-proportional hazards. This limitation has driven the deve- lopment of models that expand the analytical possibilities in survival analysis. In this context, the Generalized Time-Dependent Logistic (GTDL) family stands out as a promising alternative to the Cox model, as it allows modeling scenarios in which the proportional hazards assumption is violated. However, a relevant limitation of the GTDL family is its inability to accommodate the bathtub-shaped hazard function, a pattern frequently observed in empirical data. To address this issue, this work proposes an extension of the GTDL family, called the Extended Generalized Time-Dependent Logistic (GTDEL) family, which is capable of representing a broader range of hazard function shapes, including the bathtub form. The mathematical formulation of the new distribution is presented, along with its main theoretical properties and the construction of the associated regression model. In the literature, the GTDL model is usually considered in the case where the parameter α is positive. In this study, we emphasize the importance of investigating the model’s behavior when α < 0, thereby introducing the so-called defective versions of the GTDL and GTDEL models. Maximum likelihood estimators are derived, and their asymptotic performance is assessed through Monte Carlo simulation studies under different experimental scenarios. Finally, the proposed methodology is applied to four real datasets, among which the pbc dataset stands out, originating from a clinical study involving patients with primary biliary cirrhosis.