Survival regression with proper scoring rules and monotonic neural networks

David Rindt, Robert Hu, David Steinsaltz, Dino Sejdinovic
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:1190-1205, 2022.

Abstract

We consider frequently used scoring rules for right-censored survival regression models such as time-dependent concordance, survival-CRPS, integrated Brier score and integrated binomial log-likelihood, and prove that neither of them is a proper scoring rule. This means that the true survival distribution may be scored worse than incorrect distributions, leading to inaccurate estimation. We prove, in contrast to these scores, that the right-censored log-likelihood is a proper scoring rule, i.e. the highest expected score is achieved by the true distribution. Despite this, modern feed-forward neural-network-based survival regression models are unable to train and validate directly on right-censored log-likelihood, due to its intractability, and resort to the aforementioned alternatives, i.e. non-proper scoring rules. We therefore propose a simple novel survival regression method capable of directly optimizing log-likelihood using a monotonic restriction on the time-dependent weights, coined SurvivalMonotonic-net (SuMo-net). SuMo-net achieves state-of-the-art log-likelihood scores across several datasets with 20–100x computational speedup on inference over existing state-of-the-art neural methods and is readily applicable to datasets with several million observations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-rindt22a, title = { Survival regression with proper scoring rules and monotonic neural networks }, author = {Rindt, David and Hu, Robert and Steinsaltz, David and Sejdinovic, Dino}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {1190--1205}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/rindt22a/rindt22a.pdf}, url = {https://proceedings.mlr.press/v151/rindt22a.html}, abstract = { We consider frequently used scoring rules for right-censored survival regression models such as time-dependent concordance, survival-CRPS, integrated Brier score and integrated binomial log-likelihood, and prove that neither of them is a proper scoring rule. This means that the true survival distribution may be scored worse than incorrect distributions, leading to inaccurate estimation. We prove, in contrast to these scores, that the right-censored log-likelihood is a proper scoring rule, i.e. the highest expected score is achieved by the true distribution. Despite this, modern feed-forward neural-network-based survival regression models are unable to train and validate directly on right-censored log-likelihood, due to its intractability, and resort to the aforementioned alternatives, i.e. non-proper scoring rules. We therefore propose a simple novel survival regression method capable of directly optimizing log-likelihood using a monotonic restriction on the time-dependent weights, coined SurvivalMonotonic-net (SuMo-net). SuMo-net achieves state-of-the-art log-likelihood scores across several datasets with 20–100x computational speedup on inference over existing state-of-the-art neural methods and is readily applicable to datasets with several million observations. } }
Endnote
%0 Conference Paper %T Survival regression with proper scoring rules and monotonic neural networks %A David Rindt %A Robert Hu %A David Steinsaltz %A Dino Sejdinovic %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-rindt22a %I PMLR %P 1190--1205 %U https://proceedings.mlr.press/v151/rindt22a.html %V 151 %X We consider frequently used scoring rules for right-censored survival regression models such as time-dependent concordance, survival-CRPS, integrated Brier score and integrated binomial log-likelihood, and prove that neither of them is a proper scoring rule. This means that the true survival distribution may be scored worse than incorrect distributions, leading to inaccurate estimation. We prove, in contrast to these scores, that the right-censored log-likelihood is a proper scoring rule, i.e. the highest expected score is achieved by the true distribution. Despite this, modern feed-forward neural-network-based survival regression models are unable to train and validate directly on right-censored log-likelihood, due to its intractability, and resort to the aforementioned alternatives, i.e. non-proper scoring rules. We therefore propose a simple novel survival regression method capable of directly optimizing log-likelihood using a monotonic restriction on the time-dependent weights, coined SurvivalMonotonic-net (SuMo-net). SuMo-net achieves state-of-the-art log-likelihood scores across several datasets with 20–100x computational speedup on inference over existing state-of-the-art neural methods and is readily applicable to datasets with several million observations.
APA
Rindt, D., Hu, R., Steinsaltz, D. & Sejdinovic, D.. (2022). Survival regression with proper scoring rules and monotonic neural networks . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:1190-1205 Available from https://proceedings.mlr.press/v151/rindt22a.html.

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