Functional Decomposition and Shapley Interactions for Interpreting Survival Models

Hazard and survival functions are natural, interpretable targets in time-to-event prediction tasks such as patient survival and disease progression modeling, 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. We validate the framework on simulated data and demonstrate its utility through cancer survival applications, including multi-modal breast cancer prognosis combining histopathology with clinical features. Together, SurvFD and SurvSHAP-IQ establish an interaction- and time-aware interpretability approach for survival modeling, with broad applicability across medicine, healthcare and other time-to-event prediction tasks.