Long-Term Disease-Free Survival of Non-Metastatic Breast Cancer Patients in Iran: A Survival Model with Competing Risks Taking Cure Fraction and Frailty into Account

Document Type : Research Articles


1 Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran.

2 Department of Applied Mathematics, Shahrood University of Technology, Shahrood, Iran.

3 Cancer Research Center, Mashhad University of Medical Sciences, Mashhad, Iran.


Introduction: Survival modeling is a very important tool to detect risk factors and provide a basis for health care planning. However, cancer data may have properties leading to distorted results with routine methods. Therefore, this study aimed to cover specific factors (competing risk, cure fraction and heterogeneity) with a real dataset of Iranian breast cancer patients using a competing risk-cure-frailty model. Materials and methods: For this historical cohort study, information for 550 Iranian breast cancer patients who underwent surgery for tumor removal from 2001 to 2007 and were followed up to March 2017, was analyzed using R 3.2 software. Results: In contrast to T-stage and N-stage, hormone receptor status did not have any significant effect on the cure fraction (long-term disease-free survival). However, T-stage, N-stage and hormone receptor status all had a significant effect on short-term disease-free survival so that the hazard of loco-regional relapse or distant metastasis in cases positive for a hormone receptor was only 0.3 times that for their negative hormone receptor counterparts. The likelihood of locoregional relapse in the first quartile of follow up was nearly twice that of other quartiles. The least cumulative incidence of time to locoregional relapse was for cases with a positive hormone receptor, low N stage and low T stage. The effect of frailty term was significant in this study and a model with frailty appeared more appropriate than a model without, based on the Akaike information criterion (AIC); values for the frailty model and one without the frailty parameter were 1370.39 and 1381.46, respectively. Conclusions: The data from this study indicate ae necessity to consider competing risk, cure fraction and heterogeneity in survival modeling. The competing risk-cure-frailty model can cover complex situations with survival data.


Main Subjects

Volume 18, Issue 10
October 2017
Pages 2825-2832
  • Receive Date: 30 July 2017
  • Revise Date: 18 September 2017
  • Accept Date: 14 October 2017
  • First Publish Date: 14 October 2017