The Concordance Index decomposition: A measure for a deeper understanding of survival prediction models
This provides a deeper diagnostic tool for survival analysis researchers, though it is incremental as it builds on the existing C-index metric.
The authors tackled the problem of evaluating survival prediction models by proposing a decomposition of the Concordance Index into two components for ranking events versus events and events versus censored cases, enabling finer-grained analysis; they demonstrated its usefulness in benchmark comparisons, showing that deep learning models maintain stable performance across censoring levels while classical models deteriorate.
The Concordance Index (C-index) is a commonly used metric in Survival Analysis for evaluating the performance of a prediction model. In this paper, we propose a decomposition of the C-index into a weighted harmonic mean of two quantities: one for ranking observed events versus other observed events, and the other for ranking observed events versus censored cases. This decomposition enables a finer-grained analysis of the relative strengths and weaknesses between different survival prediction methods. The usefulness of this decomposition is demonstrated through benchmark comparisons against classical models and state-of-the-art methods, together with the new variational generative neural-network-based method (SurVED) proposed in this paper. The performance of the models is assessed using four publicly available datasets with varying levels of censoring. Using the C-index decomposition and synthetic censoring, the analysis shows that deep learning models utilize the observed events more effectively than other models. This allows them to keep a stable C-index in different censoring levels. In contrast to such deep learning methods, classical machine learning models deteriorate when the censoring level decreases due to their inability to improve on ranking the events versus other events.