Cited by 918Statistical Methods in EpidemiologyAdvanced Causal Inference TechniquesArtificial Intelligence in Healthcare

A calibration hierarchy for risk models was defined: from utopia to empirical data

Open access
Van Calster, Ben, Nieboer, Daan, Vergouwe, Yvonne, De Cock, Bavo, Pencina, Michael J., Steyerberg, Ewout W.·2016·Journal of Clinical Epidemiology

Abstract

Objective Calibrated risk models are vital for valid decision support. We define four levels of calibration and describe implications for model development and external validation of predictions.Study design and setting We present results based on simulated data sets.Results A common definition of calibration is "having an event rate of R% among patients with a predicted risk of R%," which we refer to as "moderate calibration." Weaker forms of calibration only require the average predicted risk (mean calibration) or the average prediction effects (weak calibration) to be correct. "Strong calibration" requires that the event rate equals the predicted risk for every covariate pattern. This implies that the model is fully correct for the validation setting. We argue that this is unrealistic: the model type may be incorrect, the linear predictor is only asymptotically unbiased, and all nonlinear and interaction effects should be correctly modeled. In addition, we prove that moderate calibration guarantees nonharmful decision making. Finally, results indicate that a flexible assessment of calibration in small validation data sets is problematic.Conclusion Strong calibration is desirable for individualized decision support but unrealistic and counter productive by stimulating the development of overly complex models. Model development and external validation should focus on moderate calibration.

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Crossref · 10.1016/j.jclinepi.2015.12.005

Cites

42 of 42 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 17 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    There was some miscalibration in mean risk for Examples 1-2 where the development sample was small, even though the correct underlying model formulation was estimated.

    “There was some miscalibration in mean risk for Examples 1-2 where the development sample was small, even though the correct underlying model formulation was estimated.”
    Quote in the paperNot a substantial claim
  • Findingown data

    Enlarging the development dataset alleviated the overfitting and calibration problems.

    “Enlarging the development dataset alleviated the problems (Example 4 in Table 1, Figure 1D).”
    Quote in the paperSubstantial claim
  • Findingown data

    The flexible calibration curve is more variable and hence requires more data than the calibration slope for a stable assessment.

    “The results suggest that the flexible calibration curve is more variable and hence requires more data than the calibration slope for a stable assessment.”
    Quote in the paperSubstantial claim
  • Findingown data

    Observed calibration curves will easily deviate from the diagonal line even when the model is moderately or strongly calibrated.

    “It is clear that observed calibration curves will easily deviate from the diagonal line even when the model is moderately or strongly calibrated.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    The decision curve for the true model is the best one in Example 9.

    “Nevertheless, the decision curve for the true model is the best one.”
    Quote in the paperSubstantial claim
  • May combine two claims. 14
  • Classified as probably not a substantial claim. 9
  • The quote only partly states this claim. 1
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    Findingown data

    The Example 5 model exhibits perfect strong calibration: both calibration curves and all covariate patterns coincide with the diagonal.

    “This model exhibits perfect strong calibration: both calibration curves and all covariate patterns coincide with the diagonal.”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Findingreasoning

    In Example 6, the model is weakly but not moderately calibrated on the development data.

    “Thus, the model is weakly but not moderately calibrated on the development data.”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Findingown data

    The Example 8 model exhibits perfect moderate calibration but lacks strong calibration because results per covariate pattern are scattered around the diagonal.

    “This model exhibits perfect moderate calibration but lacks strong calibration because results per covariate pattern are scattered around the diagonal.”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Findingown data

    With 10 million patients, coefficient estimates and calibration results were perfect.

    “With 10 million patients the coefficient estimates and calibration results were perfect (Table 1, Figure 1E).”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim.

    Interpretationnone given

    Strong calibration requires that the model form is correct.

    “First, strong calibration requires that the model form (e.g. a generalized linear model such as logistic regression) is correct.”
    Quote in the paperSubstantial claim
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    Interpretationreasoning

    Refitting should lead to moderate calibration, although this may also require reassessment of nonlinear effects.

    “Refitting should lead to moderate calibration, although this may also require reassessment of nonlinear effects.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Premisecitation

    In reality, the true model is unknown, may not have a generalized linear form, or may not even exist.

    “in reality, the true model is unknown, may not have a generalized linear form, or may not even exist [22].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [22] Chatfield, 1995, Model uncertainty, data mining and statistical inference, J R Stat Soc Ser A source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    Aiming for strong calibration requires the assumption that the model formulation is fully correct, and that unbiased model coefficients as well as unbiased linear predictors are obtained.

    “In sum, aiming for strong calibration requires the assumption that the model formulation is fully correct, and that unbiased model coefficients as well as unbiased linear predictors are obtained.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Interpretationreasoning

    Logistic recalibration addresses lack of weak calibration but does not guarantee moderate calibration unless all coefficients were biased by the same rate.

    “This method addresses lack of weak calibration, but does not guarantee moderate calibration unless all coefficients were biased by the same rate.”
    Quote in the paperSubstantial claim
  • May combine two claims. The quote only partly states this claim.

    Interpretationreasoning

    Moderate calibration guarantees that clinical decisions based on the model are not harmful, with Net Benefit not lower than default strategies.

    “we prove (see Appendix) that clinical utility in terms of Net Benefit will not be lower than the default strategies that either classify everyone as having the event or as not having the event.”
    • Also stated in: § 6. Moderate calibration: a pragmatic guarantee for non-harmful decision-making · plain
      “moderate calibration guarantees that decision-making based on the model is not clinically harmful.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Premisecitation

    Strong interactions or nonlinearities may lead to miscalibration in the development sample although weak calibration is perfect.

    “For example, strong interactions or nonlinearities may lead to miscalibration in the development sample although weak calibration is perfect [11].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [11] Austin, 2014, Graphical assessment of internal and external calibration of logistic regression models by using loess smoothers, Stat Med source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Interpretationnone given

    Strong calibration requires fully correct modeling of all nonlinear and non-additive effects.

    “Third, strong calibration not only requires correctly estimated regression coefficients for the main effects of model predictors, but also requires fully correct modeling of all nonlinear and non-additive effects.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    For a moderately calibrated model, among patients with an estimated risk of r%, on average r out of 100 of these patients have the event.

    “For a moderately calibrated model the following property holds, among patients with an estimated risk of % on average out of 100 of these patients have the event.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim.

    Premisecitation

    The odds of the risk threshold is the harm-to-benefit ratio, i.e. the ratio of the harm of a false positive and the benefit of a true positive classification.

    “The odds of the risk threshold is the harm-to-benefit ratio, i.e. the ratio of the harm of a false positive and the benefit of a true positive classification[21].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [21] Pauker, 1975, Therapeutic decision making: a cost-benefit analysis, N Engl J Med source

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation

    Moderate calibration prevents the model from becoming harmful, but strong calibration may further enhance clinical utility.

    “This suggests that moderate calibration prevents the model from becoming harmful [18] but that strong calibration may further enhance the model's clinical utility.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [18] Van Calster, 2015, Calibration of risk prediction models: impact on decision-analytic performance, Med Decis Making source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    Intercept adjustment addresses calibration-in-the-large but does not guarantee weak calibration.

    “This will only address calibration-in-the-large, but does not guarantee weak calibration.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

    Premisecitation

    Simple models that are moderately but not strongly calibrated often have practical advantages such as transparency or ease of use.

    “While still providing sensible risk predictions, simple models that are for example moderately but not strongly calibrated often have many practical advantages such as transparency or ease of use [33].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [33] Marewski, 2012, Heuristic decision making in medicine, Dialogues Clin Neurosci source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    At least part of the measurement error is systematic, and further thwarts the concept of the existence of a true model.

    “This means that at least part of the measurement error is systematic, and further thwarts the concept of the existence of a true model.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S2 (checkable).

    Premisecitation

    Calibration is a pivotal aspect of model performance.

    “Calibration is a pivotal aspect of model performance [2][3][4]”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [2] Steyerberg, 2009

      Not checked in the free run.

    • cites [3] Kim, 2011, Probabilistic classifiers with high-dimensional data, Biostatistics source

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    • cites [4] Pepe, 2013, Methods for evaluating prediction performance of biomarkers and tests

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    Premisecitation

    Measurement error of predictors is common and can bias regression coefficients.

    “measurement error of the predictors is in practice often ignored although it is known that this is a common phenomenon that can bias regression coefficients [28].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [28] Fuller, 1987

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Interpretationreasoning

    If the model's Net Benefit is lower than that of a default strategy, then using the model to support decision-making can be considered as clinically harmful.

    “If the model's Net Benefit is lower than that of a default strategy, then using the model to support decision-making can be considered as clinically harmful.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In previous simulations, the Hosmer-Lemeshow test showed such poor performance that it may not be recommended for routine use.

    “In previous simulations, the Hosmer-Lemeshow test showed such poor performance that it may not be recommended for routine use [7,37].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [7] Hosmer, 1997, A comparison of goodness-of-fit tests for the logistic regression model, Stat Med source

      Not checked in the free run.

    • cites [37] Hosmer, 2002, Goodness-of-fit processes for logistic regression: simulation results, Stat Med source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given

    Net Benefit accounts for the different consequences of true and false positives through the risk threshold, i.e. the risk at which one is indifferent about classifying a patient as having the event (and providing treatment) or not.

    “Net Benefit accounts for the different consequences of true and false positives through the risk threshold, i.e. the risk at which one is indifferent about classifying a patient as having the event (and providing treatment) or not.”
    Quote in the paperNot a substantial claim
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  • The paper relies on this without support.

    Calibrated risk models are vital for valid decision support.

    “Calibrated risk models are vital for valid decision support.”
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Each contradiction between two passages listed here was confirmed by an independent check.

  • Figure 5 identifies the wrong example

    Minor

    The discussion says Figure 5 compares decision curves for Example 9, the miscalibrated model. The figure caption instead identifies Example 8, which the paper describes as moderately calibrated.

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Authors
Van Calster, B., Nieboer, D., Vergouwe, Y., De Cock, B., Pencina, M. J., & Steyerberg, E. W.
Affiliations
  • Erasmus MC (NL)
  • Duke University (US)
Venue
Journal of Clinical Epidemiology
Publisher
Elsevier BV
Published
2016-06
Volume
74
Pages
167-176
ISSN
0895-4356 (ISSN-L)
OpenAlex
W2225109326
Cited by
910
References
42
Citations by year
2026: 192 · 2025: 99 · 2024: 118 · 2023: 93 · 2022: 125 · 2021: 91 · 2020: 58 · 2019: 49 · 2018: 35 · 2017: 30 · 2016: 19 · 2013: 1
FWCI
44.92
Type
journal article
Language
en
Open access
Locations
  • Journal of Clinical Epidemiology (publishedVersion)
  • PubMed (publishedVersion)
  • Lirias (KU Leuven) (submittedVersion, other-oa)
  • EUR Research Repository (Erasmus University Rotterdam) (submittedVersion)
Funders
  • Fonds Wetenschappelijk Onderzoek (G049312N)
  • KU Leuven (C24/15/037)
  • Vlaamse regering (G049312N, C24/15/037)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
  • Health Sciences › Health Professions › Health Information Management › Artificial Intelligence in Healthcare
Keywords
risk model calibration, external validation, decision support, overfitting, simulation study
MeSH terms
Calibration, Computer Simulation, Decision Support Techniques, Humans, Risk, Reproducibility of Results, Models, Statistical, Bias, Risk Assessment

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