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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| Vydané v: | Artificial intelligence in medicine Ročník 148; s. 102781 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.02.2024
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| 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. |
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| AbstractList | 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. 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 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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| Cites_doi | 10.1016/j.eswa.2023.120218 10.1186/s12874-018-0482-1 10.1016/j.artmed.2011.06.006 10.1002/sim.2427 10.1002/sim.4154 10.1109/JBHI.2021.3052441 10.1111/1467-9876.00165 10.7326/0003-4819-122-3-199502010-00007 10.1002/sim.4780111409 10.2307/2090408 10.1016/j.artmed.2019.06.001 10.1214/08-AOAS169 10.1001/jama.1982.03320430047030 10.1371/journal.pcbi.1003047 10.1111/j.2517-6161.1972.tb00899.x 10.1088/1742-6596/1827/1/012066 10.1080/01621459.1958.10501452 10.1002/sim.3743 10.1002/(SICI)1097-0258(19960229)15:4<361::AID-SIM168>3.0.CO;2-4 10.1145/3214306 10.1093/biomet/92.4.965 10.1016/j.mayocp.2012.03.009 |
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| Keywords | Survival analysis Variational encoder–decoder Evaluation metric Concordance Index |
| Language | English |
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| Title | The Concordance Index decomposition: A measure for a deeper understanding of survival prediction models |
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