Pancreas Transplantation Outcome Predictions—PTOP: A Risk Prediction Tool for Pancreas and Pancreas-Kidney Transplants Based on a European Cohort

Background. For patients with complicated type 1 diabetes having, for example, hypoglycemia unawareness and end-stage renal disease because of diabetic nephropathy, combined pancreas and kidney transplantation (PKT) is the therapy of choice. However, the shortage of available grafts and complex impact of risk factors call for individualized, impartial predictions of PKT and pancreas transplantation (PT) outcomes to support physicians in graft acceptance decisions. Methods. Based on a large European cohort with 3060 PKT and PT performed between 2006 and 2021, the 3 primary patient outcomes time to patient mortality, pancreas graft loss, and kidney graft loss were visualized using Kaplan-Meier survival curves. Multivariable Cox proportional hazards models were developed for 5- and 10-y prediction of outcomes based on 26 risk factors. Results. Risk factors associated with increased mortality included previous kidney transplants, rescue allocations, longer waiting times, and simultaneous transplants of other organs. Increased pancreas graft loss was positively associated with higher recipient body mass index and donor age and negatively associated with simultaneous transplants of kidneys and other organs. Donor age was also associated with increased kidney graft losses. The multivariable Cox models reported median C-index values were 63% for patient mortality, 62% for pancreas loss, and 55% for kidney loss. Conclusions. This study provides an online risk tool at https://riskcalc.org/ptop for individual 5- and 10-y post-PKT and PT patient outcomes based on parameters available at the time of graft offer to support critical organ acceptance decisions and encourage external validation in independent populations.


Model selection strategy
To identify interactions of risk factors needed to be considered for model selection, Cox proportional hazards models (CPH) were fitted for each pairwise combination and each outcome.
The models included the two respective main effects and their interaction.If the interaction showed a p-value below 0.001, it was considered for the respective outcomes.Hence, for patient survival, we added the interaction between a simultaneous kidney transplant and previous kidney transplants as well as the interaction between simultaneous kidney transplant and recipient age.For the kidney outcome, we added the interaction between previous kidney transplants and recipient BMI.For pancreas survival, no interactions showed a p-value small enough to be added.
Multivariable Cox regression was used for all outcomes, including interactions where necessary.
To determine the best model for the risk prediction of the three outcomes, repeatedly sampled cross-validation (RSCV) with ten iterations and five folds was used, whereby for each iteration, the data were randomly split into five distinct groups.For each fold, one validation dataset

Results of model comparison
Comparison of the C index values over all iterations and folds of the RSCV approach to find the most suitable selection and fitting method showed that almost all methods had very similar results, however, there were isolated downward outliers (Supplementary Figure 1).Additionally, these results were compared with non-imputed validation datasets and obtained comparable results for the median, however, the results showed large variances in particular for methods using all covariates.We selected the BIC method for our models because it had some of the highest median C index values for all three outcomes, needed only few risk factors, and thus showed a comparably small variance between the values of the C index.
For the final models, the covariate combinations were used, which had been selected most often by the BIC method.For patient mortality, four combinations of risk factors were selected equally often (12%).We therefore chose the combination of time on the waiting list, indicators of allocation type, previous kidney transplants, simultaneous transplant of other organs, simultaneous transplant of a kidney, and the interaction between simultaneous kidney transplant and recipient age.With regards to pancreas loss, donor age, recipient BMI, and indicators of simultaneous transplant of other organs and simultaneous transplant of a kidney were the dominant combination with 28%.For kidney loss, the risk factors were donor age and the interaction between previous kidney transplants and recipient BMI.This combination was selected in 42% of the cases.Overall, the selected combinations indicated the difference between the most predictive risk factors for the three outcomes and showed the importance of a differentiated investigation.
consisting of one of the five groups was withheld for testing and one training dataset consisting of the other groups was used for training the model.Imputed versions of the training and validation datasets using multiple imputations by chained equations blinded to outcome were used to account for missing values.All the modeling techniques were trained on the imputed training set and the corresponding C index was calculated based on the validation set.To select the most suitable modeling approach, C index values over all iterations and folds as well as the number of used risk factors were compared.For the chosen method, the most often selected combination of incorporated risk factors was then selected as the final model for each respective outcome.The prediction methods were the full CPH model using all predictor values, the stepwise selection CPH model with the Akaike information criterion, the stepwise CPH model with the Bayesian information criterion (BIC), the CPH model with an adaptive elastic-net penalty, the random forest model, the model-based boosting CPH model, and the DeepSurv neural network.

Figure S2 :
Figure S2: Calibration plots of predicted and observed risks ten years post-transplant