Multi-state analysis of kidney transplant recipients outcome: a semi-Markov model for studying the role of pre-transplant sensitization against Angiotensin II Type 1 receptor.


  • Florence Gillaizeau
  • Magali Giral
  • Etienne Dantan
  • Duska Dragun
  • Jean-Paul Soulillou
  • Yohann Foucher


Chronic diseases are characterized by their long duration and generally their slow progression. To study the time to several stages of progression, traditional survival analyses are not appropriate and the use of multi-state models is required. Of these, the Semi-Markov model (SMM) is convenient because it considers that the probability that a patient goes from a state to another depends on the time already spent in this state. In this paper, we illustrate the interest of using a SMM by re-analysing the data of an observational study which was designed to investigate the relationship between the pre-graft level of the angiotensin II type 1 receptor antibodies (AT1R-Abs) and the evolution of kidney transplant recipients (KTR). Previous results were obtained by a multivariate Cox proportional hazards model and showed that patients with high pre-graft level of AT1R-Abs seemed to have more risk of early acute rejection episodes (ARE) and return to dialysis after 3 years post-transplantation. Nevertheless, it was not possible to distinguish whether AT$_{1}$R-Abs had a direct correlation with the graft failure or if this correlation went through an increased incidence of ARE. Thus, a four-state model is proposed to study the graft without any ARE, the graft with at least one ARE, the return in dialysis and the patient death. 599 KTR transplanted in Nantes University Hospital between 1998 and 2007 were included. The baseline hazard functions of the sojourn time distributions were modelled using the generalized Weibull distribution. At the time of the study, 403 (67%) patients had a functional graft without ARE whereas 105 (15%) patients returned to dialysis, 64 (11%) patients had an ARE and 50 (8%) patients died with a functional graft. Taking into account of traditional factors associated to the recipient's evolution, a high pre-graft level of AT1R-Abs (>=10U) was associated to an increased risk of ARE. For patients without ARE, there was no evidence of association between the pre-graft level of AT1R-Abs and the risk of graft failure within the first 3 years following the transplantation. In contrast, a high pre-graft level of AT1R-Abs seemed to increase this risk beyond 3 years post-transplantation. Finally, the association between the pre-graft level of AT1R-Abs and the time to death was not significant. The goodness-of-fit of the SMM to our data seemed correct. This study shows the SMMs are particularly adapted to investigate the relationship between a biomarker and the evolution of disease. These models offer additional information to physicians/scientists about the mechanistic associated to a biomarker. The biostatistical community underutilizes these models, which is counter-productive regarding the original results they offer in translational research. Further efforts are needed to promote such models to biostatisticians to expand their daily use.






Numéro spécial : données longitudinales quantitatives, événementielles, incomplètement observées