Prognostic Factors Associated with Curing in Patients with Breast Cancer: A Joint Frailty Model

Recurrent event data arise frequently in longitudinal medical studies. In many situations, there are a large portion of patients without any recurrences, manifesting the "zero-inflated" nature of the data. Moreover, there often exists a terminal event which may be correlated with the recurrent events. The goal of this study is to extend the application of joint frailty model to identify the prognostic factors associated with curing in patients with breast cancer.

As a prospective study, medical records of women who had been attended to Cancer Research Center, Shahid Beheshti University of Medical Sciences from January 1998 to February 2016 were reviewed. Finally, after an initial review of medical records, 711 patients were included in the study and analyzed. A checklist that included items drawn from the demographic background of patients was provided in the study. Two joint frailty models for zero-inflated recurrent events, combining a logistic model for "structural zero" status (Yes/No) and a joint frailty proportional hazards model for recurrent and terminal event times were performed to identify factors associated with BCS.

The mean age of patients was 38.2 years. The numbers of subjects with 1, 2, 3, and 4 recurrent events were 392, 207, 97, and 15, respectively. The median follow-up time was 6.87 years. There were 137 (19.2%) deaths from cancer during the follow-up. Among the 574 patients who were censored, 418 had no tumor recurrence. Thus, there may exist a large portion of "cured" subjects. We can see that the radiation (OR = 6.02, CI = (3.87, 8.61)) and tumor size interaction with radiation (OR = 1.065, CI = (1.002-1.26)) were significant in the cure model (P < 0.05) which means that patients with smaller tumor sizes were more likely to be cured by radiation therapy.

Our proposed models can help investigators to evaluate which treatment will result in a higher fraction of cured subjects. This is usually an important research question in biomedical studies.