  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.
