A competing risks cure frailty model: An application to relapse-free survival of breast cancer patients

In competing risks cure models, if there is unobserved heterogeneity among susceptible patients, application of the methods that do not consider this heterogeneity, may lead to invalid results. Therefore, this study aimed to introduce a model to cover the above properties of survival studies. We introduced a unified model by combining a parametric mixture cure gamma frailty model and vertical modeling of competing risks. We obtained estimates of parameters by an iterative method and Laplace transform technique. Then, we calculated the cumulative incidence functions (CIFs) and related confidence bounds by using a bootstrap approach. We conducted an extensive simulation study to evaluate the performance of the proposed model. The results of the simulation study showed the superior performance of our proposed competing risks cure frailty model. Finally, we applied the proposed method to analyze a real dataset of breast cancer patients.

[1]  J. P. Sy,et al.  Estimation in a Cox Proportional Hazards Cure Model , 2000, Biometrics.

[2]  M. A. Nicolaie,et al.  Vertical modeling: analysis of competing risks data with a cure fraction , 2019, Lifetime data analysis.

[3]  Gregg E. Dinse,et al.  A mixture model for the regression analysis of competing risks data , 1985 .

[4]  Daniel Commenges,et al.  A penalized likelihood approach for mixture cure models , 2009, Statistics in medicine.

[5]  S. Bull,et al.  Elevated expression of podocalyxin is associated with lymphatic invasion, basal-like phenotype, and clinical outcome in axillary lymph node-negative breast cancer , 2013, Breast Cancer Research and Treatment.

[6]  K. Yonemori,et al.  Use of Cox's Cure Model to Establish Clinical Determinants of Long-Term Disease-Free Survival in Neoadjuvant-Chemotherapy-Treated Breast Cancer Patients without Pathologic Complete Response , 2013, International journal of breast cancer.

[7]  K. Dear,et al.  A Nonparametric Mixture Model for Cure Rate Estimation , 2000, Biometrics.

[8]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[9]  Chao Cai.  Advanced Methodology Developments in Mixture Cure Models , 2013 .

[10]  M A Nicolaie,et al.  Vertical modelling: Analysis of competing risks data with missing causes of failure , 2015, Statistical methods in medical research.

[11]  Anthony Y. C. Kuk,et al.  A mixture model combining logistic regression with proportional hazards regression , 1992 .

[12]  M. Yaseri,et al.  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 , 2017, Asian Pacific journal of cancer prevention : APJCP.

[13]  V. Farewell,et al.  The use of mixture models for the analysis of survival data with long-term survivors. , 1982, Biometrics.

[14]  ARTZNER Philippe.  Cure frailty models for survival data : Application to recurrences for breast cancer and to hospital readmissions for colorectal cancer , 2012 .

[15]  J. Boag,et al.  Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy , 1949 .

[16]  Robert Gray,et al.  A Proportional Hazards Model for the Subdistribution of a Competing Risk , 1999 .

[17]  Xuelin Huang,et al.  Efficient semiparametric mixture inferences on cure rate models for competing risks , 2015 .

[18]  Joseph Berkson,et al.  Survival Curve for Cancer Patients Following Treatment , 1952 .

[19]  P. Lambert,et al.  The Application of Cure Models in the Presence of Competing Risks: A Tool for Improved Risk Communication in Population-Based Cancer Patient Survival , 2014, Epidemiology.

[20]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.

[21]  Johann Sölkner,et al.  Frailty Models in Survival Analysis , 1996 .

[22]  B. Rasmussen,et al.  Prognostic effect of estrogen receptor status across age in primary breast cancer , 2007, International journal of cancer.

[23]  M A Nicolaie,et al.  Vertical modeling: A pattern mixture approach for competing risks modeling , 2010, Statistics in medicine.

[24]  Melania Pintilie,et al.  Focus on : Contemporary Methods in Biostatistics ( II ) An Introduction to Competing Risks Analysis , 2017 .

[25]  C. Osborne,et al.  Diseases of the breast: Fifth edition , 2014 .

[26]  R. Maller,et al.  Survival Analysis with Long-Term Survivors , 1996 .

[27]  M S Pepe,et al.  Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data? , 1993, Statistics in medicine.

[28]  R. Tiwari,et al.  Breast cancer survival, competing risks and mixture cure model: a Bayesian analysis , 2010 .