Enhancing Visual Interpretability and Explainability in Functional Survival Trees and Forests

TL;DR

This work tackles the interpretability gap in functional survival modelling by introducing graphical interpretability (LFSDC) for Functional Survival Trees and time-aware explainability (SurvSHAP with global PFI) for Functional Random Survival Forests. It leverages FPCA via PACE to handle irregular longitudinal data and uses survival-specific splits to reveal how functional covariates shape survival over time. The proposed LFSDC, node-separability metrics, SurvSHAP(t), and time-aware global-local importance measures are validated on simulations and an SOFA-case study, illustrating clearer, clinically actionable insights into time-to-event processes with functional predictors. The framework advances XAI in healthcare by delivering transparent, time-resolved interpretations for complex functional survival models, enabling more informed risk assessment and decision-making.

Abstract

Functional survival models are key tools for analyzing time-to-event data with complex predictors, such as functional or high-dimensional inputs. Despite their predictive strength, these models often lack interpretability, which limits their value in practical decision-making and risk analysis. This study investigates two key survival models: the Functional Survival Tree (FST) and the Functional Random Survival Forest (FRSF). It introduces novel methods and tools to enhance the interpretability of FST models and improve the explainability of FRSF ensembles. Using both real and simulated datasets, the results demonstrate that the proposed approaches yield efficient, easy-to-understand decision trees that accurately capture the underlying decision-making processes of the model ensemble.

Figures (17)

• Figure 1: Visualization of time-dependent covariates and estimated trajectories for $N=200$ (Upper) and $N=300$ (Lower) stratified by censoring status and event occurrence.
• Figure 2: Visualisation of the separation regions in the root node for two different sample sizes, $N = 200$ (left) and $N = 300$ (right).
• Figure 3: Survival dynamics of distance at each level for $\mathcal{A}^*_h$ nodes of FMST for $N=200$ (left) and $N=300$ (right)
• Figure 4: Visualization of simulated results for two different sample sizes. The top row corresponds to the case $N=200$ observations: on the left, the FMST, while on the right, a portion of the FMST is displayed in its functional form, highlighting the separation spaces in $\mathcal{L}^2(\mathcal{T})$ norm and the graphical sets at the terminal nodes. The bottom row presents the same layout for a sample $N=300$.
• Figure 5: Graphical representation of SOFA scores and estimated trajectory over time stratified by outcome.