Multivariate Joint Frailty Models for Modeling Multiple Recurrent Events and Its Application in Breast Cancer

Breast cancer is one of the most common recurrence cancers among women. There are several factors that can affect the multiple recurrence of this disease, which have been studied and recognized in various studies, however, with the fact that these factors are known, cannot always accurately predict the incidence of metastasis. On the other hand, simultaneous examination of the types of relapses will make the results more accurate. One of the types of models used to analyze recurrent events with heterogeneity among patients is a frailty model. The purpose of this study was to use a joint frailty model to model multiple recurrences in breast cancer patients data. In this retrospective study, 342 breast cancer patients whose records were registered at the Shohada Tajrish Hospital Cancer Research Center were investigated. Patients were monitored for at least 6 months after diagnosis, and their last condition was recorded. For data analysis, the joint frailty survival model was used. Data modeling and data analysis were done in R software. The three-year and five-year survival rates for patients were respectively 0.79 and 0.68 respectively. According to the results of the fitted joint frailty model, it can be said that the risk of multiple recurrence (local and metastasis) is increased for patients with tumor grade greater than I. We also found that if we did not consider the relationship between multiple recurrence in patients with breast cancer, we would lose significant correlation. Considering the significant variance of the frailty component of the metastasis event, it can be concluded that patients with the same predictor variables also have a different metastasis risk and, on the other hand, given the low frequency of types of recurrences in this study, the results should be considered with caution.