Soft decision trees for survival analysis
This paper addresses key limitations of conventional survival trees—namely, local optimization, poor interpretability, and inflexibility in modeling survival functions. We propose the Soft Survival Tree (SST), a novel framework that jointly optimizes tree structure and smooth survival functions (parametric, semiparametric, or nonparametric) at leaf nodes. SST is the first to integrate soft splitting with maximum-likelihood-based survival modeling while preserving conditional independence. It employs a node-wise decomposition optimization algorithm, adapted from Consolo et al. (2024), enabling global parameter optimization. Additionally, SST supports group fairness extensions. Evaluated on 15 benchmark datasets, SST consistently outperforms three state-of-the-art survival tree methods across four metrics: C-index, Integrated Brier Score (IBS), Brier Score, and Calibration (CAL) Score—demonstrating superior discriminative ability and calibration accuracy. Crucially, SST retains clinical interpretability and offers enhanced modeling flexibility.