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


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.

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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.

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Correspondence to Yohann Foucher.

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Trébern-Launay, K., Kessler, M., Bayat-Makoei, S. et al. Horizontal mixture model for competing risks: a method used in waitlisted renal transplant candidates. Eur J Epidemiol 33, 275–286 (2018).

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  • Competing events
  • Mixture model
  • Kidney transplantation
  • Prognostic study