Functional Decomposition and Shapley Interactions for Interpreting Survival Models

TL;DR

This paper introduces a new interpretability framework for survival models that decomposes feature effects over time and extends Shapley interactions to handle time-dependent effects, addressing limitations of traditional additive explanations.

Contribution

The paper presents SurvFD for decomposing feature effects in survival models and SurvSHAP-IQ for estimating time-dependent feature interactions, advancing interpretability in survival analysis.

Findings

SurvFD reveals when additive explanations fail in survival models.

SurvSHAP-IQ effectively estimates higher-order, time-dependent interactions.

The approach improves understanding of feature effects over time in survival prediction.

Abstract

Hazard and survival functions are natural, interpretable targets in time-to-event prediction, but their inherent non-additivity fundamentally limits standard additive explanation methods. We introduce Survival Functional Decomposition (SurvFD), a principled approach for analyzing feature interactions in machine learning survival models. By decomposing higher-order effects into time-dependent and time-independent components, SurvFD offers a previously unrecognized perspective on survival explanations, explicitly characterizing when and why additive explanations fail. Building on this theoretical decomposition, we propose SurvSHAP-IQ, which extends Shapley interactions to time-indexed functions, providing a practical estimator for higher-order, time-dependent interactions. Together, SurvFD and SurvSHAP-IQ establish an interaction- and time-aware interpretability approach for survival modeling, with broad applicability across time-to-event prediction tasks.