Advancing Survival Prediction with Functional Random Survival Forests for Time-to-Event Data

This paper proposes an improved way to handle survival learning for time-to-event data by combining Functional Data Analysis (FDA) [1] with Random Survival Forests (RSF) [2]. Traditional survival models often have trouble dealing with complex, irregular, and censored functional data. To fix this, we introduce Censored Functional Data (CFD) [3], which captures each subject’s data only up to the earliest of the event or censoring time, avoiding excessive interpolation and better representing the real data. Using Functional Principal Component Analysis (FPCA) [4] and optimizing how time is discretized, our Functional Random Survival Forest (FRSF) framework efficiently models survival data that’s irregularly observed. We tested it through simulations with different baseline hazard functions and found that the CFD-based FRSF outperforms traditional survival models, delivering better prediction accuracy measured by Continuous Ranked Probability Score (CRPS) and Requested Performance Error (RPE). Also, variable importance analysis shows that the CFD model uses a wider range of principal components, which boosts interpretability and robustness. Overall, our method offers a flexible, nonparametric approach for survival analysis with complex functional predictors, improving both predictive performance and understanding of time-to-event data.