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

A Statistical Learning Take on the Concordance Index for Survival Analysis