Modelos de sobrevivência bivariados induzidos por fragilidade

Abstract

Frailty models have been developed to quantify both heterogeneity as well as association in multivariate time-to-event data. The frailty distributions used in many studies include the gamma, inverse Gaussian (IG) or stable positive (SP) distributions. These distributions are usually chosen due to analytical and computational simplicity or due to some attractive property of the model. The choice of the frailty distribution is of fundamental importance in order to arrive at a good description of the dependence structure present in the data. An alternative to the problem of choosing the frailty model would be to choose only one family of frailty distributions and use it as a general model. In this work, we studied bivariate survival data with a semicompetiting risk structure (FINE; JIANG; CHAPPELL, 2001), and long-term bivariate data. In order to incorporate a dependence structure between the times of events, we propose the family of distributions Power variance function (PVF) as a shared frailty model which includes the above mentioned distributions. Data with a semicompeting risk structure arises as a variant of the competing risk structure. In the semicompeting risk framework, usually, two events are considered, namely, a terminal and a non-terminal. The terminal event censors the non-terminal event, but not vice versa. Generally, the two events are correlated. So the dependence between the terminal and non-terminal failure time is incorporated through the PVF shared frailty between the conditional transition rates of the illness-death model (XU; KALBFLEISCH; TAI, 2010), that is equivalent to a semicompeting risks problem. For long-term bivariate data, which are characterized by having a fraction of individuals non-susceptible to the event of interest after a long time, were considered situations in which there are two types of unobservable causes, where each cause is related to occurrence times of an event of interest. To model the dependence between the two times we introduce a PVF frailty variable. For both models, a simulation study is presented to evaluate the performance of the maximum likelihood method in the parameters estimation. Finally, colon cancer data are used in the application of the model with a semicompeting risk structure and Brazilian customer churn data in a financial institution are used in the application of the long-term models.