Prognostic Factors of Long-term Survival among Rheumatic Heart Disease using Standard versus Cox Proportional Hazard Mixture Cure Model


  • Nurhasniza Idham Abu Hasan
  • Nor Azura Md.Ghani
  • Khairul Asri Mohd Ghani
  • Khairul Izan Mohd Ghani
  • Nurhasnira Abu Hasan





Cox Proportional Hazard Cure Model, Long-Term Survival, Prognostic Factors, Rheumatic Heart Disease, Standard Cox Proportional Hazard Model


The mixture cure model brings a great interest among researchers to the analyses survival data in the presence of cured. This study highlighted the importance of cured to be considered when the study population consists of two different type of groups.  In such situations, the appropriate model is warranted. In this work, the standard Cox Proportional Hazard (PH) model and Cox PH mixture cure model were employed in order to highlight the difference and the usefulness of the mixture cure model over standard model. The Rheumatic Heart Disease (RHD) dataset could be applied for this purpose. Results—The cured fraction was estimated to be 93.7%. The cure analysis shows the effect of Coronary Pulmonary Bypass (P-value=0.015), Mitral procedure (P-value=0.067) and Age (P-value=0.035) were significantly associated with cured among the RHD patients.  Meanwhile, the length of hospital stay (P-value=0.055) and older age (P-value=0.063) were significantly associated with uncured patients. However, the standard Cox PH model do not allow to discriminate the effects of prognostic factors between these two different patients. The results reveled that HPT (P-value<0.030), emergency Intra Operative status (P-value=0.001), Mitral valve procedures (P-value=0.031), CPB (P-value=0.000), HOSP (<6 days groups) (P-value=0.020) and Redo Post-Operative status (P-value=0.002) were identified as factors associated with the time to death among patients. Conclusion— The results exhibited the advantages of mixture cure model over standard survival model when the cured present in the data.




[1] D.R. Cox, Regression Models and Life-Table, Journal of the Royal Statistical Society: Series B (Methodological), 34(2)(1972),187-220.

[2] G. T. Le, M. Abrahamowicz, P. Bolard and C. Quantin, Comparison of Cox's and relative survival models when estimating the effects of prognostic factors on disease-specific mortality: a simulation study under proportional excess hazards, Stat Med., 24(24):3887-909.

[3] A.M.R. Bakar, K.A. Salah, N.A. Ibrahim, et al. Cure fraction, modelling and estimating in a population-based cancer survival analysis, Malaysian J Mathematical Sciences, 2(2008),113-134.

[4] M. Othus, B. Barlogie, M.L. Leblanc, and J.J. Crowley, Cure models as a useful statistical tool for analysing survival, Clinical Research Research, 18 (2012),3731–3736.

[5] V.T. Farewell, The use of mixture models for the analysis of survival data with long-term survivors, Biometrics, 38(4)(1982),1041–1046.

[6] A.Y.C. Kuk, and C.H. Chen, A mixture model combining logistic regression and proportional hazards regression, Biometrika, 79(1992)531–541.

[7] J.P. Sy, and J.M.G. Taylor, Estimation in a Cox proportional hazards cure model, Biometrics, 56(1)(2000),227–236.

[8] R. Sposto, Cure model analysis in cancer: An application to data from the children’s cancer group, Stat Med, 21(2002),293-312.

[9] A. Sashegyi, & D. Ferrya. On the Interpretation of the Hazard Ratio and Communication of Survival Benefit. The Oncologist, 22(2017), 484–486.

[10] J. Asano, A. Hirakawa, C. Hamada, K. Yonemori, T. Hirata, C. Shimizu, 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. Int J Breast Cancer, 2013 (2013), 1-9.

[11] E.P. Wileyto, Y. Li, J. Chen, & D.F. Heitjan. Assessing the fit of parametric cure models. Biostat., 14(2(2013), 340–350.

[12] S. Maetani, and J.M. Gamel, Parametric Cure Model versus Proportional Hazards Model in Survival Analysis of Breast Cancer and Other Malignancies, Advances in Breast Cancer Research, 2(2013)119-125.

[13] D. Wang, and M. Murphy, Use of a mixture model for the analysis of contraceptive-use duration among long-term users, Journal of Applied Statistics, 25(3)(1998)319-332

[14] S. Chauvaud, J.F. Fuzellier, A. Berrebi, A. Deloche, J.N. Fabiani, and A. Carpentier, Long-Term (29 Years) Results of Reconstructive Surgery in Rheumatic Mitral Valve Insufficiency, Circulation, 104(2001),I-12-I-15.

[15] C.M. Vassileva, G. Mishkel, C. McNeely, T. Boley, S. Markwell, S. Scaife, and S. Hazelrigg, Long-term survival of patients undergoing mitral valve repair and replacement: a longitudinal analysis of medicare fee-for-service beneficiaries, Circulation, 127(2013),1870-1876.

[16] J.B. Kim, H.J. Kim, D.H. Moon, S.H. Jung, S.J. Choo, C.H. Chung, H. Song, and J.W. Lee, Long-term outcomes after surgery for rheumatic mitral valve disease: valve repair versus mechanical valve replacement, European Journal of Cardio-thoracic Surgery,37(2010),1039—1046.

[17] M.A. Yakub, J. Dillon, P.S.K. Moorthy, K.K Pau, and M.N. Nordin, Is rheumatic aetiology a predictor of poor outcome in the current era of mitral valve repair? Contemporary long-term results of mitral valve repair in rheumatic heart disease, European journal of cardio-Thoracic surgery, 44(2013)673-681.

[18] D. Mohty, T.A. Orzulak, H.V. Schaff, J.F. Avierinos, J.A. Tajif, and M. Enriquez-Sarano, Very long-term survival and durability of mitral valve repair for mitral valve prolapsed, Circulation, 1041(2001)11-17.

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