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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Veröffentlicht in:	Artificial intelligence in medicine Jg. 148; S. 102781
Hauptverfasser:	Alabdallah, Abdallah, Ohlsson, Mattias, Pashami, Sepideh, Rögnvaldsson, Thorsteinn
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Netherlands Elsevier B.V 01.02.2024
Schlagworte:	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
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Abstract	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.
AbstractList	The Concordance Index (C-index) is a commonly used metric in Survival Analysis for evaluating the performance of a prediction model. This paper proposes 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 more fine-grained analysis of the strengths and weaknesses of survival prediction methods. The usefulness of this decomposition is demonstrated through benchmark comparisons against state-of-the-art and classical models, together with a new variational generative neural-network-based method (SurVED), which is also proposed in this paper. Performance is assessed using four publicly available datasets with varying levels of censoring. The analysis using the C-index decomposition and synthetic censoring shows that deep learning models utilize the observed events more effectively than other models, allowing them to keep a stable C-index in different censoring levels. In contrast, classical machine learning models deteriorate when the censoring level decreases due to their inability to improve on ranking the events versus other events. © 2024 The Author(s) 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 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. 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 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 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.
ArticleNumber	102781
Author	Ohlsson, Mattias Alabdallah, Abdallah Pashami, Sepideh Rögnvaldsson, Thorsteinn
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Keywords	Survival analysis Variational encoder–decoder Evaluation metric Concordance Index
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Snippet	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... The Concordance Index (C-index) is a commonly used metric in Survival Analysis for evaluating the performance of a prediction model. This paper proposes a...
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SubjectTerms	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
Title	The Concordance Index decomposition: A measure for a deeper understanding of survival prediction models
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