A Statistical Learning Take on the Concordance Index for Survival Analysis

Kevin Elgui, Alex Nowak, Geneviève Robin
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:4712-4731, 2023.

Abstract

The introduction of machine learning (ML) techniques to the field of survival analysis has increased the flexibility of modeling approaches, and ML based models have become state-of-the-art. These models optimize their own cost functions, and their performance is often evaluated using the concordance index (C-index). From a statistical learning perspective, it is therefore an important problem to analyze the relationship between the optimizers of the C-index and those of the ML cost functions. We address this issue by providing C-index Fisher-consistency results and excess risk bounds for several of the commonly used cost functions in survival analysis. We identify conditions under which they are consistent, under the form of three nested families of survival models. We also study the general case where no model assumption is made and present a new, off-the-shelf method that is shown to be consistent with the C-index, although computationally expensive at inference. Finally, we perform limited numerical experiments with simulated data to illustrate our theoretical findings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-elgui23a, title = {A Statistical Learning Take on the Concordance Index for Survival Analysis}, author = {Elgui, Kevin and Nowak, Alex and Robin, Genevi\`eve}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {4712--4731}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/elgui23a/elgui23a.pdf}, url = {https://proceedings.mlr.press/v206/elgui23a.html}, abstract = {The introduction of machine learning (ML) techniques to the field of survival analysis has increased the flexibility of modeling approaches, and ML based models have become state-of-the-art. These models optimize their own cost functions, and their performance is often evaluated using the concordance index (C-index). From a statistical learning perspective, it is therefore an important problem to analyze the relationship between the optimizers of the C-index and those of the ML cost functions. We address this issue by providing C-index Fisher-consistency results and excess risk bounds for several of the commonly used cost functions in survival analysis. We identify conditions under which they are consistent, under the form of three nested families of survival models. We also study the general case where no model assumption is made and present a new, off-the-shelf method that is shown to be consistent with the C-index, although computationally expensive at inference. Finally, we perform limited numerical experiments with simulated data to illustrate our theoretical findings.} }
Endnote
%0 Conference Paper %T A Statistical Learning Take on the Concordance Index for Survival Analysis %A Kevin Elgui %A Alex Nowak %A Geneviève Robin %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-elgui23a %I PMLR %P 4712--4731 %U https://proceedings.mlr.press/v206/elgui23a.html %V 206 %X The introduction of machine learning (ML) techniques to the field of survival analysis has increased the flexibility of modeling approaches, and ML based models have become state-of-the-art. These models optimize their own cost functions, and their performance is often evaluated using the concordance index (C-index). From a statistical learning perspective, it is therefore an important problem to analyze the relationship between the optimizers of the C-index and those of the ML cost functions. We address this issue by providing C-index Fisher-consistency results and excess risk bounds for several of the commonly used cost functions in survival analysis. We identify conditions under which they are consistent, under the form of three nested families of survival models. We also study the general case where no model assumption is made and present a new, off-the-shelf method that is shown to be consistent with the C-index, although computationally expensive at inference. Finally, we perform limited numerical experiments with simulated data to illustrate our theoretical findings.
APA
Elgui, K., Nowak, A. & Robin, G.. (2023). A Statistical Learning Take on the Concordance Index for Survival Analysis. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:4712-4731 Available from https://proceedings.mlr.press/v206/elgui23a.html.

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