Methods: To model renal transplant survival, we developed three Cox proportional-hazards regression models for: 1) patient mortality, 2) graft failure with return to hemodialysis and 3) failure and return to peritoneal dialysis. Based on 5,471 first and second transplants in patients from the Dutch End-Stage Renal Disease Registry, we computed transition probabilities by using the baseline cumulative hazard and the linear predictor equations summing the covariates to compute a cycle-specific instantaneous baseline hazard for each of the three Cox models. Per cycle these three hazards were summed and the total hazard was used to calculate the total transition probability. Subsequently, patients were distributed across states according to the ratio of each of the three hazards divided by the total hazard. We compared the survival curves resulting from a Cox model containing all three events with the Markov model curves for four scenarios defined by age and transplant-type.

Results: The survival curves from the Cox and the Markov models were comparable. One-year survival as estimated with the Markov model as compared with the Cox model for 30- and 60-year-old patients with deceased donor kidneys were 89.4% vs 88.1% and 84.3% vs 81.1%. For 30- and 60-year-old patients with living-donor kidneys these were 93.6% vs 92.0% and 88.0% vs 87.0%. The results were closer when comparing the three hazard functions separately. Of the four scenarios, the 60-year-old patients with diseased donor kidneys showed the most divergent results, e.g. 1-year patient mortality was 9.2% for the Cox vs 8.3% for the Markov model.

Discussion: Our method for translating Cox regression models into Markov models in the presence of competing risks yielded consistent results. Residual differences may be due to the following:(1) the Cox survival curve was based on one hazard function that combines all events whereas the Markov curve was based on the combination of three separate hazard functions and (2) continuous follow-up time from the Cox models was divided into discrete intervals in the Markov model.