FunCQNet: A Functional Censored Quantile Neural Network for Predicting Long-Term Post-Transplant Kidney Survival

Accurate survival prediction in kidney transplantation is critical yet challenging due to the complex interplay between functional biomarkers and patient characteristics under censoring. To address this, we propose a functional censored quantile neural network (FunCQNet), a novel framework that integrates deep neural networks with a censoring-adjusted sequential quantile loss to approximate interaction-dependent coefficient functions. We further introduce a conformal inference approach to rigorously assess the significance of functional-scalar interactions, ensuring interpretability alongside predictive power. Extensive simulations demonstrate that FunCQNet robustly recovers functional effects under varying noise and censoring levels. When applied to kidney transplant data, the model yields precise multi-quantile predictions and reveals clinically significant, age-dependent interaction patterns between donor type and recipient survival.

Kidney transplantation can greatly improve the lives of patients with kidney failure, but predicting how long a patient will survive after transplantation remains difficult. One important signal is the patient’s kidney function over time, measured by eGFR, but this signal is not a single number: it is a changing curve during the years after transplant. Its meaning can also differ across patients, depending on factors such as age, sex, and whether the kidney came from a living or deceased donor. We propose FunCQNet, a machine learning method that uses these kidney-function trajectories together with patient and donor information to predict post-transplant survival. Instead of producing only one average prediction, our method estimates several possible survival levels, giving a more complete picture of risk and uncertainty. It also learns how the effect of kidney-function changes may vary across patient subgroups. Applied to kidney transplant data, FunCQNet identifies meaningful interaction patterns, especially involving donor type and age, and provides individualized survival predictions. This can help clinicians better understand patient-specific risks and support more personalized post-transplant monitoring and care.