The Concordance Index decomposition: A measure for a deeper understanding of survival prediction models

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,...

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Bibliographic Details
Published in:Artificial intelligence in medicine Vol. 148; p. 102781
Main Authors: Alabdallah, Abdallah, Ohlsson, Mattias, Pashami, Sepideh, Rögnvaldsson, Thorsteinn
Format: Journal Article
Language:English
Published: Netherlands Elsevier B.V 01.02.2024
Subjects:
artificial neural network
Bioinformatics
Computer
Concordance Index
Deep learning
Encoder-decoder
Evaluation Metric
Evaluation metrics
Fine-grained analysis
Forecasting
Learning systems
Machine Learning
Matematik
Mathematical Sciences
Natural Sciences
Naturvetenskap
Neural Networks
Prediction modelling
Probability Theory and Statistics
Sannolikhetsteori och statistik
Signal encoding
Survival Analysis
Survival prediction
Variational Encoder-Decoder
Weighted harmonic means
Survival analysis
Variational encoder–decoder
Evaluation metric
Concordance Index
ISSN:0933-3657, 1873-2860, 1873-2860
Online Access:Get full text
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Summary: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. •The C-Index Decomposition is proposed as a weighted harmonic mean of the C-index of the events vs other events and the C-index of events vs censored cases.•The C-Index Decomposition gives a more detailed image of the survival model performance.•SurVED; a new survival model based on Variational inference formulation was shown to be better at improving performance with more observed event.•Models which seem to perform similarly using the C-index, showed different behavior with respect to the terms of the C-index decomposition.
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ISSN:0933-3657
1873-2860
1873-2860
DOI:10.1016/j.artmed.2024.102781