Cited by 48Statistical Methods in EpidemiologyStatistical Methods and InferenceMeta-analysis and systematic reviews

A new concordance measure for risk prediction models in external validation settings

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van Klaveren, David, Gönen, Mithat, Steyerberg, Ewout W., Vergouwe, Yvonne·2016·Statistics in Medicine

Abstract

Concordance measures are frequently used for assessing the discriminative ability of risk prediction models. The interpretation of estimated concordance at external validation is difficult if the case‐mix differs from the model development setting. We aimed to develop a concordance measure that provides insight into the influence of case‐mix heterogeneity and is robust to censoring of time‐to‐event data. We first derived a model‐based concordance (mbc) measure that allows for quantification of the influence of case‐mix heterogeneity on discriminative ability of proportional hazards and logistic regression models. This mbc can also be calculated including a regression slope that calibrates the predictions at external validation (c‐mbc), hence assessing the influence of overall regression coefficient validity on discriminative ability. We derived variance formulas for both mbc and c‐mbc. We compared the mbc and the c‐mbc with commonly used concordance measures in a simulation study and in two external validation settings. The mbc was asymptotically equivalent to a previously proposed resampling‐based case‐mix corrected c‐index. The c‐mbc remained stable at the true value with increasing proportions of censoring, while Harrell's c‐index and to a lesser extent Uno's concordance measure increased unfavorably. Variance estimates of mbc and c‐mbc were well in agreement with the simulated empirical variances. We conclude that the mbc is an attractive closed‐form measure that allows for a straightforward quantification of the expected change in a model's discriminative ability due to case‐mix heterogeneity. The c‐mbc also reflects regression coefficient validity and is a censoring‐robust alternative for the c‐index when the proportional hazards assumption holds. Copyright © 2016 John Wiley & Sons, Ltd.

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  • An additional advantage of IPD is that it becomes possible to adjust discrimination performance for (variation in) subject-level covariates, and thus to gain more understanding in sources of between-study heterogeneity.

    “An additional advantage of IPD is that it becomes possible to adjust discrimination performance for (variation in) subject-level covariates, and thus to gain more understanding in sources of between-study heterogeneity.9,10,26,68”

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Authors
van Klaveren, D., Gönen, M., Steyerberg, E. W., & Vergouwe, Y.
Affiliations
  • Department of Public Health Erasmus University Medical Center Rotterdam The Netherlands
  • Memorial Sloan Kettering Cancer Center (US)
  • Erasmus MC (NL)
Venue
Statistics in Medicine
Publisher
Wiley
Published
2016-06
Volume
35
Issue
23
Pages
4136-4152
ISSN
  • 0277-6715 (ISSN-L)
  • 1097-0258
OpenAlex
W2417826452
Cited by
48
References
24
Citations by year
2026: 2 · 2025: 2 · 2024: 8 · 2023: 2 · 2022: 12 · 2021: 9 · 2020: 3 · 2019: 5 · 2018: 2 · 2017: 3
FWCI
3.37
Type
journal article
Language
en
Open access
Locations
  • Statistics in Medicine (publishedVersion)
  • PubMed (publishedVersion)
  • EUR Research Repository (Erasmus University Rotterdam) (publishedVersion)
  • Europe PMC (PubMed Central) (acceptedVersion)
  • PubMed Central (acceptedVersion)
  • EUR Research Repository (Erasmus University Rotterdam) (submittedVersion)
Funders
Netherlands Organisation for Scientific Research (917.11.383.)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
Keywords
concordance measures, risk prediction model, external validation, concordance index, Harrell's C-index, censoring, time-to-event data, proportional hazards model, logistic regression, forecast calibration, discriminatory power, variance estimation
MeSH terms
Diagnosis-Related Groups, Humans, Models, Statistical, Logistic Models

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