European Journal of Epidemiology

, Volume 33, Issue 3, pp 275–286 | Cite as

Horizontal mixture model for competing risks: a method used in waitlisted renal transplant candidates

  • Katy Trébern-Launay
  • Michèle Kessler
  • Sahar Bayat-Makoei
  • Anne-Hélène Quérard
  • Serge Briançon
  • Magali Giral
  • Yohann FoucherEmail author


When a patient is registered on renal transplant waiting list, she/he expects a clear information on the likelihood of being transplanted. Nevertheless, this event is in competition with death and usual models for competing events are difficult to interpret for non-specialists. We used a horizontal mixture model. Data were extracted from two French dialysis and transplantation registries. The “Ile-de-France” region was used for external validation. The other patients were randomly divided for training and internal validation. Seven variables were associated with decreased long-term probability of transplantation: age over 40 years, comorbidities (diabetes, cardiovascular disease, malignancy), dialysis longer than 1 year before registration and blood groups O or B. We additionally demonstrated longer mean time-to-transplantation for recipients under the age of 50, overweight recipients, recipients with blood group O or B and with pre-transplantation anti-HLA class I or II immunization. Our model can be used to predict the long-term probability of transplantation and the time in dialysis among transplanted patients, two easily interpretable parts. Discriminative capacities were validated on both the internal and external (AUC at 5 years = 0.72, 95% CI from 0.68 to 0.76) validation samples. However, calibration issues were highlighted and illustrated the importance of complete re-estimation of the model for other countries. We illustrated the ease of interpretation of horizontal modelling, which constitutes an alternative to sub-hazard or cause-specific approaches. Nevertheless, it would be useful to test this in practice, for instance by questioning both the physicians and the patients. We believe that this model should also be used in other chronic diseases, for both etiologic and prognostic studies.


Competing events Mixture model Kidney transplantation Prognostic study 



This work was supported by grants from the French Ministry of Health (PHRC, PROG/11/85, 2011) and the French National Agency of Research (ANR-II- JSV1-0008-01). K. Trébern-Launay was also the recipient of a grant for epidemiology and biostatistics research from the RTRS ‘CENTAURE’. We wish to thank the members of The French Réseau Epidémiologie et Information en Néphrologie (REIN) Registry, the French Cristal Registry and the Nephrolor network.

Supplementary material

10654_2017_322_MOESM1_ESM.docx (626 kb)
Supplementary material 1 (DOCX 626 kb)


  1. 1.
    Wolfe RA, Ashby VB, Milford EL, Ojo AO, Ettenger RE, Agodoa LY, et al. Comparison of mortality in all patients on dialysis, patients on dialysis awaiting transplantation, and recipients of a first cadaveric transplant. N Engl J Med. 1999;341:1725–30.CrossRefPubMedGoogle Scholar
  2. 2.
    Tonelli M, Wiebe N, Knoll G, Bello A, Browne S, Jadhav D, et al. Systematic review: kidney transplantation compared with dialysis in clinically relevant outcomes. Am J Transpl Off J Am Soc Transpl Am Soc Transpl Surg. 2011;11:2093–109.CrossRefGoogle Scholar
  3. 3.
    Wong G, Howard K, Chapman JR, Chadban S, Cross N, Tong A, et al. Comparative survival and economic benefits of deceased donor kidney transplantation and dialysis in people with varying ages and co-morbidities. PLoS ONE. 2012;7:e29591.CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Satayathum S, Pisoni RL, McCullough KP, Merion RM, Wikström B, Levin N, et al. Kidney transplantation and wait-listing rates from the international Dialysis Outcomes and Practice Patterns Study (DOPPS). Kidney Int. 2005;68:330–7.CrossRefPubMedGoogle Scholar
  5. 5.
    Danovitch GM, Cohen DJ, Weir MR, Stock PG, Bennett WM, Christensen LL, et al. Current status of kidney and pancreas transplantation in the United States, 1994–2003. Am J Transpl Off J Am Soc Transpl Am Soc Transpl Surg. 2005;5:904–15.CrossRefGoogle Scholar
  6. 6.
    Li PK-T, Chu KH, Chow KM, Lau MF, Leung CB, Kwan BCH, et al. Cross sectional survey on the concerns and anxiety of patients waiting for organ transplants. Nephrol. Carlton Vic. 2012;17:514–8.Google Scholar
  7. 7.
    Akman B, Uyar M, Afsar B, Sezer S, Ozdemir FN, Haberal M. Adherence, depression and quality of life in patients on a renal transplantation waiting list. Transpl. Int. Off. J. Eur. Soc. Organ Transplant. 2007;20:682–7.Google Scholar
  8. 8.
    Davison SN. The ethics of end-of-life care for patients with ESRD. Clin. J. Am. Soc. Nephrol. CJASN. 2012;7:2049–57.CrossRefPubMedGoogle Scholar
  9. 9.
    Vandecasteele SJ, Kurella Tamura M. A patient-centered vision of care for ESRD: dialysis as a bridging treatment or as a final destination? J. Am. Soc. Nephrol. JASN. 2014;25:1647–51.CrossRefPubMedGoogle Scholar
  10. 10.
    Fine JP, Gray RJ. A Proportional Hazards Model for the Subdistribution of a Competing Risk. J Am Stat Assoc. 1999;94:496–509.CrossRefGoogle Scholar
  11. 11.
    Prentice RL, Kalbfleisch JD, Peterson AV, Flournoy N, Farewell VT, Breslow NE. The analysis of failure times in the presence of competing risks. Biometrics. 1978;34:541–54.CrossRefPubMedGoogle Scholar
  12. 12.
    Cox D. Regression models and life-tables. J. R. Stat. Soc. Ser. B. 1972;34:187–229.Google Scholar
  13. 13.
    Andersen PK, Geskus RB, Witte T de, Putter H. Competing risks in epidemiology: possibilities and pitfalls. Int. J. Epidemiol. 2012;dyr213.Google Scholar
  14. 14.
    Sapir-Pichhadze R, Pintilie M, Tinckam KJ, Laupacis A, Logan AG, Beyene J, et al. Survival Analysis in the Presence of Competing Risks: The Example of Waitlisted Kidney Transplant Candidates. Am J Transplant. 2016;16:1958–66.CrossRefPubMedGoogle Scholar
  15. 15.
    Fuller R, Dudley N, Blacktop J. Risk communication and older people—understanding of probability and risk information by medical inpatients aged 75 years and older. Age Ageing. 2001;30:473–6.CrossRefPubMedGoogle Scholar
  16. 16.
    Larson MG, Dinse GE. A Mixture Model for the Regression Analysis of Competing Risks Data. Appl Stat. 1985;34:201.CrossRefGoogle Scholar
  17. 17.
    Checkley W, Brower RG, Muñoz A. Inference for Mutually Exclusive Competing Events Through a Mixture of Generalized Gamma Distributions. Epidemiology. 2010;21:557–65.CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    Lau B, Cole SR, Gange SJ. Competing risk regression models for epidemiologic data. Am J Epidemiol. 2009;170:244–56.CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    Empirical Transition Matrix of Multi-State Models: The etm Package| Allignol| Journal of Statistical Software [Internet]. [cited 2016 Mar 7]. Available from:
  20. 20.
    Foucher Y, Danger R. Time dependent ROC curves for the estimation of true prognostic capacity of microarray data. Stat Appl Genet Mol Biol. 2012;11:Article 1.Google Scholar
  21. 21.
    Blanche P, Dartigues J-F, Jacqmin-Gadda H. Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks. Stat Med. 2013;32:5381–97.CrossRefPubMedGoogle Scholar
  22. 22.
    R Development Core Team. R: A Language and Environment for Statistical Computing [Internet]. Computing RF for S, editor. Vienna, Austria; 2010. Available from:
  23. 23.
    Geskus RB. Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics. 2011;67:39–49.CrossRefPubMedGoogle Scholar
  24. 24.
    Murphy DJ, Burrows D, Santilli S, Kemp AW, Tenner S, Kreling B, et al. The Influence of the Probability of Survival on Patients’ Preferences Regarding Cardiopulmonary Resuscitation. N Engl J Med. 1994;330:545–9.CrossRefPubMedGoogle Scholar
  25. 25.
    Andersen PK, Keiding N. Interpretability and importance of functionals in competing risks and multistate models. Stat Med. 2012;31:1074–88.CrossRefPubMedGoogle Scholar
  26. 26.
    Henderson R, Keiding N. Individual survival time prediction using statistical models. J Med Ethics. 2005;31:703–6.CrossRefPubMedPubMedCentralGoogle Scholar
  27. 27.
    Hollnagel H. Explaining risk factors to patients during a general practice consultation. Conveying group-based epidemiological knowledge to individual patients. Scand J Prim Health Care. 1999;17:3–5.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Centre de Recherche en Transplantation et immunologue, UMR 1064INSERM, Université de NantesNantesFrance
  2. 2.Institut de Transplantation Urologie NephrologieCHU NantesNantesFrance
  3. 3.Université de Nantes, Université de Tours, INSERM, SPHERE (INSERM U1246): methodS in Patient-centered outcomes and HEalth ResEarch - IRS2NantesFrance
  4. 4.Fondation CentaureNantesFrance
  5. 5.Nephrology UnitNancy-Brabois University HospitalVandœuvre-lès-NancyFrance
  6. 6.Epidemiology and Biostatistics UnitEHESP School of Public HealthRennesFrance
  7. 7.Nephrology Hemodialysis, TransplantationVendée Departmental HospitalLa Roche sur YonFrance
  8. 8.Clinical EpidemiologyINSERM CIC-EC, Nancy-Brabois University Hospital, Vandoeuvre-lès-Nancy, Lorraine University, and Paris Descartes UniversityNancyFrance
  9. 9.CHU NantesNantesFrance

Personalised recommendations