On Ranking in Survival Analysis: Bounds on the Concordance Index

Abstract

In this paper, we show that classical survival analysis involving censored data can naturally be cast as a ranking problem. The concordance index (CI), which quantifies the quality of rankings, is the standard performance measure for model assessment in survival analysis. In contrast, the standard approach to learning the popular proportional hazard (PH) model is based on Cox's partial likelihood. In this paper we devise two bounds on CI--one of which emerges directly from the properties of PH models--and optimize them directly. Our experimental results suggest that both methods perform about equally well, with our new approach giving slightly better results than the Cox's method. We also explain why a method designed to maximize the Cox's partial likelihood also ends up (approximately) maximizing the CI.

Tasks

Reproductions