Functional Decomposition and Shapley Interactions for Interpreting Survival Models

Sophie Hanna Langbein, Hubert Baniecki, Fabian Fumagalli, Niklas Koenen, Marvin N. Wright, Julia Herbinger
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:62603-62641, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-langbein26a, title = {Functional Decomposition and Shapley Interactions for Interpreting Survival Models}, author = {Langbein, Sophie Hanna and Baniecki, Hubert and Fumagalli, Fabian and Koenen, Niklas and Wright, Marvin N. and Herbinger, Julia}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {62603--62641}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/langbein26a/langbein26a.pdf}, url = {https://proceedings.mlr.press/v306/langbein26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Functional Decomposition and Shapley Interactions for Interpreting Survival Models %A Sophie Hanna Langbein %A Hubert Baniecki %A Fabian Fumagalli %A Niklas Koenen %A Marvin N. Wright %A Julia Herbinger %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-langbein26a %I PMLR %P 62603--62641 %U https://proceedings.mlr.press/v306/langbein26a.html %V 306 %X 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.
APA
Langbein, S.H., Baniecki, H., Fumagalli, F., Koenen, N., Wright, M.N. & Herbinger, J.. (2026). Functional Decomposition and Shapley Interactions for Interpreting Survival Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:62603-62641 Available from https://proceedings.mlr.press/v306/langbein26a.html.

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