23º SINAPE - Simpósio Nacional de Probabilidade e Estatística

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Analysis of Semi-competing Risks Data Using Illness–Death Processes with shared frailty: Application in Colon Cancer data


The semi-competing risks situation is a generalization of competing risks and usually one considers only two events, one terminal and one non-terminal. In this situation the terminal event censors the non-terminal event, while the occurrence of the non-terminal event does not prevent the terminal event from occurring. Typically, the two events are correlated. We consider an illness–death model with shared frailty, suggested Xu et. al (2010), which in its most restrictive form is identical to the semi-competing risks model. In their model the dependency between the terminal and non-terminal failure time is incorporated through the use of a shared frailty, which gives a model with conditional transition rates possessing the Markov property. We introduce the use of a parametric model for the conditional transition rates. Maximum likelihood estimation is performed to fit the model to data set. Then the model is applied to a data-set on a colon cancer clinical trial (Moertel et al., 1990).


Copula; Dependent censoring; Frailty; Illness–death model; Proportional hazards; Semi-competing risks data; Terminal event.


Análise de Sobrevivência


Elizbeth Chipa Bedia , Vicente Garibay Cancho