Modelos multiestado com fragilidade

Abstract

Often intermediate events provide more detailed information about the disease process or recovery, for example, and allow greater accuracy in predicting the prognosis of patients. Such non-fatal events during the course of the disease can be seen as transitions from one state to another. The basic idea of a multistate models is that the person moves through a series of states in continuous time, it is possible to estimate the transition probabilities and intensities between them and the effect of covariates associated with each transition. Many studies include the grouping of survival times, for example, in multi-center studies, and is also of interest to study the evolution of patients over time, characterizing grouped multistate data. Because the data coming from different centers/groups, the failure times these individuals are grouped and the common risk factors not observed, it is interesting to consider the use of frailty so that we can capture the heterogeneity between the groups at risk for different types of transition, in addition to considering the dependence structure between transitions of individuals of the same group. In this work we present the methodology of multistate models, frailty models and then the integration of models with multi-state fragility models, dealing with the process of parametric and semi-parametric estimation. The conducted simulation study showed the importance of considering frailty in grouped multistate models, because without considering them, the estimates become biased. Furthermore, we find the frequentist properties of estimators of multistate model with nested frailty. Finally, as an application example to a set of real data, we use the process of bone marrow transplantation recovery of patients in four hospitals.We did a comparison of models through quality teasures setting AIC and BIC, coming to the conclusion that the model considers two random effects (one for the hospital and another for interaction transition-hospital) fits the data better. In addition to considering the heterogeneity between hospitals, such a model also considers the heterogeneity between hospitals in each transition. Thus, the values of the frailty estimated interaction transition-hospital reveal how fragile patients from each hospital are to experience certain type of event/transition.