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.