Exploring the Wasserstein metric for time-to-event analysis

Tristan Sylvain, Margaux Luck, Joseph Cohen, Heloise Cardinal, Andrea Lodi, Yoshua Bengio
Proceedings of AAAI Spring Symposium on Survival Prediction - Algorithms, Challenges, and Applications 2021, PMLR 146:194-206, 2021.

Abstract

Survival analysis is a type of semi-supervised task where the target output (the survival time) is often right-censored. Utilizing this information is a challenge because it is not obvious how to correctly incorporate these censored examples into a model. We study how three categories of loss functions can take advantage of this information: partial likelihood methods, rank methods, and our own classification method based on a Wasserstein metric (WM) and the non-parametric Kaplan Meier (KM) estimate of the probability density to impute the labels of censored examples. The proposed method predicts the probability distribution of an event, letting us compute survival curves and expected times of survival that are easier to interpret than the rank. We also demonstrate that this approach directly optimizes the expected C-index which is the most common evaluation metric for survival models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v146-sylvain21a, title = {Exploring the Wasserstein metric for time-to-event analysis}, author = {Sylvain, Tristan and Luck, Margaux and Cohen, Joseph and Cardinal, Heloise and Lodi, Andrea and Bengio, Yoshua}, booktitle = {Proceedings of AAAI Spring Symposium on Survival Prediction - Algorithms, Challenges, and Applications 2021}, pages = {194--206}, year = {2021}, editor = {Greiner, Russell and Kumar, Neeraj and Gerds, Thomas Alexander and van der Schaar, Mihaela}, volume = {146}, series = {Proceedings of Machine Learning Research}, month = {22--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v146/sylvain21a/sylvain21a.pdf}, url = {https://proceedings.mlr.press/v146/sylvain21a.html}, abstract = {Survival analysis is a type of semi-supervised task where the target output (the survival time) is often right-censored. Utilizing this information is a challenge because it is not obvious how to correctly incorporate these censored examples into a model. We study how three categories of loss functions can take advantage of this information: partial likelihood methods, rank methods, and our own classification method based on a Wasserstein metric (WM) and the non-parametric Kaplan Meier (KM) estimate of the probability density to impute the labels of censored examples. The proposed method predicts the probability distribution of an event, letting us compute survival curves and expected times of survival that are easier to interpret than the rank. We also demonstrate that this approach directly optimizes the expected C-index which is the most common evaluation metric for survival models.} }
Endnote
%0 Conference Paper %T Exploring the Wasserstein metric for time-to-event analysis %A Tristan Sylvain %A Margaux Luck %A Joseph Cohen %A Heloise Cardinal %A Andrea Lodi %A Yoshua Bengio %B Proceedings of AAAI Spring Symposium on Survival Prediction - Algorithms, Challenges, and Applications 2021 %C Proceedings of Machine Learning Research %D 2021 %E Russell Greiner %E Neeraj Kumar %E Thomas Alexander Gerds %E Mihaela van der Schaar %F pmlr-v146-sylvain21a %I PMLR %P 194--206 %U https://proceedings.mlr.press/v146/sylvain21a.html %V 146 %X Survival analysis is a type of semi-supervised task where the target output (the survival time) is often right-censored. Utilizing this information is a challenge because it is not obvious how to correctly incorporate these censored examples into a model. We study how three categories of loss functions can take advantage of this information: partial likelihood methods, rank methods, and our own classification method based on a Wasserstein metric (WM) and the non-parametric Kaplan Meier (KM) estimate of the probability density to impute the labels of censored examples. The proposed method predicts the probability distribution of an event, letting us compute survival curves and expected times of survival that are easier to interpret than the rank. We also demonstrate that this approach directly optimizes the expected C-index which is the most common evaluation metric for survival models.
APA
Sylvain, T., Luck, M., Cohen, J., Cardinal, H., Lodi, A. & Bengio, Y.. (2021). Exploring the Wasserstein metric for time-to-event analysis. Proceedings of AAAI Spring Symposium on Survival Prediction - Algorithms, Challenges, and Applications 2021, in Proceedings of Machine Learning Research 146:194-206 Available from https://proceedings.mlr.press/v146/sylvain21a.html.

Related Material