Análise de sobrevivência na presença de censura informativa: uma abordagem Bayesiana

Abstract

Most procedures found in the literature to model survival data are based on the assumption of non-informative censoring mechanism, meaning that failure and censored times are independent. Although independence is a model assumption, testing this condition requires additional data which are often unavailable. In several real situations this assumption is not valid and the censoring mechanism is thus called informative. An alternative for data modeling under censoring mechanism is based on the inclusion of a random effect known as frailty, which influences both failure and censoring times. In this study, two Bayesian models are proposed: in one of them, the frailty effect is related to the censoring times through a parameter, the other one considers a mixture distribution to model the frailty effect. These models can indicate the type of association and, consequently, the censoring mechanism of the data. A simulated study, focused on the Weibull distribution, considering different failure proportions, sample sizes and correlation type between failure and censoring was developed to compare the performances of some model specifications: (i) without frailty, (ii) with frailty only on the failure component, (iii) frailty in both components and affected by a censoring parameter, (iv) with frailty in both components but affecting the censoring via mixture. Finally, the models are applied to real data.