Evaluation of performance measures in predictive artificial intelligence models to support medical decisions: overview and guidance

In the paper

“Estimated probabilities with too much spread are on average too close to 0 and 1 (slope < 1), whereas estimated probabilities with too little spread are on average too close to the prevalence (slope > 1).”

What the sources say

• Partly supported

  Section 2.1 (page unavailable) says overfitting produces predictions that are too extreme: high risks are overestimated and low risks underestimated. It also identifies the calibration slope as an indicator of overfitting or underfitting, but our copy does not explicitly state that underfitted probabilities are too close to the prevalence; the numerical slope thresholds are missing from its rendered equations. (LLM, conf=0.78)

  cites [52] Van Calster, 2016, A calibration hierarchy for risk models was defined: from utopia to empirical data, J Clin Epidemiol sourceExperimental — accuracy not yet measured
• Not checked yetcites [53] Stevens, 2020, Validation of clinical prediction models: what does the “calibration slope” really measure?, J Clin Epidemiol source

In the paper

“There were 434 women with a malignant tumour (prevalence 49%). 32”

What the sources say

• Supported

  The Patient and tumour characteristics section states that the primary analysis included 894 patients, of whom 434 (49%) had a malignant tumour. This directly matches the cited claim. (LLM, conf=0.95)

  cites [32] Landolfo, 2024, Comparison of the ADNEX and ROMA risk prediction models for the diagnosis of ovarian cancer: a multicentre external validation in patients who underwent surgery, Br J Cancer source

In the paper

“The ADNEX model had an AUROC of 0 ⋅ 91 (95% CI 0 ⋅ 89-0 ⋅ 93) and an AUPRC of 0 ⋅ 89 (95% CI 0 ⋅ 86-0 ⋅ 91).”

In the paper

“The calibration intercept of the ADNEX model was 0 ⋅ 81 (95% CI 0 ⋅ 62-1 ⋅ 01), suggesting underestimation of probabilities on average (intercept > 0).”

In the paper

“Ignoring sensitivity values below 0 ⋅ 8, pAUROC was 0 ⋅ 14 (95% CI 0 ⋅ 13-0 ⋅ 15).”

In the paper

“A probable reason is that fi ve of six participating centres in the validation study were tertiary care centres, resulting in a high prevalence of malignancy (49%).”

In the paper

“17 measures showed both characteristics, 14 showed one, and one (F1 score) showed neither.”

In the paper

“Some partial classification measures improved (sensitivity and NPV), whereas others worsened (specificity and PPV).”

In the paper

“At a threshold of 10%, the ADNEX model showed a classification accuracy of 0 ⋅ 79 (95% CI 0 ⋅ 77-0 ⋅ 82), F1 score of 0 ⋅ 82 (0 ⋅ 79-0 ⋅ 84), and MCC of 0 ⋅ 63 (0 ⋅ 58-0 ⋅ 67) (table 1).”

In the paper

“At the commonly recommended threshold of 10% in our case study, 23 ADNEX classified 578 patients as high risk, of whom 414 had a malignant tumour (true positive) and 164 had a benign tumour (false positive). The remaining 316 patients were classified as low risk, of whom 296 had a benign tumour (true negative) and 20 had a malignant tumour (false negative).”

What the sources say

• Not checked yetcites [23] Timmerman, 2021, ESGO/ISUOG/IOTA/ESGE consensus statement on preoperative diagnosis of ovarian tumors, Ultrasound Obstet Gynecol source

In the paper

“For example, calibration is an active area of research focusing on aspects such as strong calibration, quantifying the degree of miscalibration, and uncertainty.”

What the sources say

• Not checked yetcites [62] Arrieta-Ibarra, 2022, Metrics of calibration for probabilistic predictions, J Mach Learn Res
• Not checked yetcites [113] Perez-Lebel, 2022, Beyond calibration: estimating the grouping loss of modern neural networks, arXiv
• Not checked yetcites [114] Kompa, 2021, Second opinion needed: communicating uncertainty in medical machine learning, NPJ Digit Med source
• Not checked yetcites [115] Riley, 2023, Stability of clinical prediction models developed using statistical or machine learning methods, Biom J source

In the paper

“If misclassification costs influence a performance measure in an implicit or ad hoc way, the measure neither assesses statistical performance nor adequately evaluates the quality of decisions for clinical practice.”

In the paper

“Discrimination reflects relative performance; ie, it does not matter how high or low the estimated probabilities are, only whether they allow to discriminate between individuals with versus without the event.”

In the paper

“Classification performance is influenced by discrimination and calibration performance.”

In the paper

“Using statistical arguments to set a decision threshold is inconsistent with decision theory and detached from practical use by clinicians.”

In the paper

“Statistical performance measures are essential for model evaluation but cannot be used to fi nd out whether a model should be used in practice: it is not appropriate to cite, for example, good discrimination and calibration or conclude that a model can be used to aid decisions about ovarian surgery.”

In the paper

“The fi fth domain, clinical utility, goes one step further by explicitly incorporating misclassification costs when evaluating classifications of individuals into low-risk and high-risk groups.”

In the paper

“Among these domains, the fi rst three evaluate performance based on probability estimates (Appendix p 2).”

In the paper

“When an incorrect model can have a better expected value than the correct model, the measure is termed improper and cannot be trusted.”

In the paper

“The importance of properness is that a proper measure cannot be fooled: in expectation, the correct model cannot be outperformed by an incorrect one.”

In the paper

“The fourth and fi fth performance domains require a threshold on the estimated risk of the event to classify individuals into two mutually exclusive groups: low-risk (estimated risk below the threshold) and high-risk (estimated risk equal to or above the threshold) groups.”

In the paper

“Measures that do not possess the fi rst characteristic cannot be trusted, whereas measures not possessing the second are equivocal.”

In the paper

“poorly performing models might lead to wrong clinical decisions that can be detrimental to patients and increase fi nancial costs. 5”

What the sources say

• Not checked yetcites [5] Kamran, 2024, Evaluation of sepsis prediction models before onset of treatment, NEJM AI source

In the paper

“Calibration reflects absolute performance by evaluating whether estimates are too high or too low.”

In the paper

“Models can therefore have good discrimination but poor calibration, and vice versa.”

In the paper

“The definition of discrimination implies that discrimination measures should rely only on the ranks of the estimated probabilities in the dataset. 36”

What the sources say

• Not checked yetcites [36] Berrar, 2012, Caveats and pitfalls of ROC analysis in clinical microarray research (and how to avoid them), Brief Bioinform source

In the paper

“Research on the quantification of a fourth level, strong calibration, is ongoing.”

In the paper

“A decision threshold of 0 ⋅ 1 (10%) for the probability of malignancy is often recommended. 23”

What the sources say

• Not checked yetcites [23] Timmerman, 2021, ESGO/ISUOG/IOTA/ESGE consensus statement on preoperative diagnosis of ovarian tumors, Ultrasound Obstet Gynecol source

In the paper

“Discrimination measures are not meant to reflect differential misclassification costs, and class imbalance should not be conflated with misclassification costs or medical relevance.”

In the paper

“ADNEX was developed on the data from 5909 individuals recruited between 1999 and 2012 in 24 secondary and tertiary care centres from 10 countries (Italy, Belgium, Sweden, Czech Republic, Poland, France, United Kingdom, China, Spain, and Canada).”

What the sources say

• Not checked yetcites [31] Van Calster, 2014, Evaluating the risk of ovarian cancer before surgery using the ADNEX model to differentiate between benign, borderline, early and advanced stage invasive, and secondary metastatic tumours: prospective multicentre diagnostic study, BMJ source

In the paper

“The model can inform decisions regarding the type of surgery (advanced vs conservative) for patients examined at an oncology centre or regarding referral to an oncology centre for patients examined elsewhere. 32”

What the sources say

• Not checked yetcites [32] Landolfo, 2024, Comparison of the ADNEX and ROMA risk prediction models for the diagnosis of ovarian cancer: a multicentre external validation in patients who underwent surgery, Br J Cancer source

In the paper

“This method is thus a rank-preserving method, and the ranking of patients based on the estimated probability of malignancy remains the same before and after updating.”

In the paper

“The weight of these consequences might vary by the nature and effects of the intervention, the health-care system, or by clinician and patient.”

In the paper

“Further, ECE, ECI, and ICI depend on the grouping or smoothing methods used and have issues with statistical consistency.”

What the sources say

• Not checked yetcites [62] Arrieta-Ibarra, 2022, Metrics of calibration for probabilistic predictions, J Mach Learn Res

In the paper

“it is not appropriate to cite, for example, good discrimination and calibration or conclude that a model can be used to aid decisions about ovarian surgery.”

In the paper

“Often, however, a threshold is chosen by optimising a statistical measure such as the Youden index (sensitivity + specificity -1).”

In the paper

“discrimination slope and mean absolute prediction error are improper.”

What the sources say

• Not checked yetcites [26] Buja
• Not checked yetcites [27] Gneiting, 2007, Strictly proper scoring rules, prediction, and estimation, J Am Stat Assoc source
• Not checked yetcites [71] Van Houwelingen, 2012

In the paper

“Although true negatives might be highly irrelevant for selected non-medical applications, such errors are generally important in medical applications.”

In the paper

“Nevertheless, although discriminatory ability is essential for predictive AI, AUROC alone cannot be used to identify a model as good or useful. 51”

What the sources say

• Not checked yetcites [51] de Hond, 2022, Interpreting area under the receiver operating characteristic curve, Lancet Digit Health source

In the paper

“This method is similar to Platt scaling, a well known method in machine learning to improve the calibration of predictions. 34,35”

What the sources say

• Not checked yetcites [34] Ojeda, 2023, Calibrating machine learning approaches for probability estimation: a comprehensive comparison, Stat Med source
• Not checked yetcites [35] Platt, 1999, Probabilistic outputs for support vector machines and comparison to regularized likelihood methods

In the paper

“The TransIOTA study externally validated ADNEX for its ability to distinguish benign from malignant tumours, using data from 894 women recruited between 2015 and 2019 in one secondary and five tertiary care centres in four countries (Belgium, Italy, Czech Republic, and United Kingdom).”

What the sources say

• Not checked yetcites [32] Landolfo, 2024, Comparison of the ADNEX and ROMA risk prediction models for the diagnosis of ovarian cancer: a multicentre external validation in patients who underwent surgery, Br J Cancer source

In the paper

“In biomedical applications, the consequences of a false negative (for instance, not referring a woman with ovarian malignancy for advanced surgery) are almost always different from the consequences of a false positive (referring a woman with a benign tumour for advanced surgery).”

In the paper

“AUPRC and pAUROC mix statistical performance with aspects of clinical utility without following decision-analytical principles.”

In the paper

“For binary outcomes, the C-statistic is equal to area under the receiver operating characteristic curve (AUROC). 37,38”

What the sources say

• Not checked yetcites [37] Bradley, 1997, The use of the area under the ROC curve in the evaluation of machine learning algorithms, Pattern Recognit source
• Not checked yetcites [38] Verbakel, 2020, ROC curves for clinical prediction models part 1. ROC plots showed no added value above the AUC when evaluating the performance of clinical prediction models, J Clin Epidemiol source

In the paper

“Loglikelihood, logloss, and Brier score are strictly proper”

What the sources say

• Not checked yetcites [26] Buja
• Not checked yetcites [27] Gneiting, 2007, Strictly proper scoring rules, prediction, and estimation, J Am Stat Assoc source
• Not checked yetcites [71] Van Houwelingen, 2012

In the paper

“These approaches can be classified into three increasingly stringent levels, labelled as mean, weak, and moderate calibration. 52”

What the sources say

• Not checked yetcites [52] Van Calster, 2016, A calibration hierarchy for risk models was defined: from utopia to empirical data, J Clin Epidemiol source

In the paper

“AUROC, AUPRC, and pAUROC are semi-proper, because these rank-based measures are invariant to monotonic transformations of probability estimates. 48”

What the sources say

• Not checked yetcites [48] Pepe, 2015, The Net Reclassification Index (NRI): a misleading measure of prediction improvement even with independent test data sets, Stat Biosci source

In the paper

“When maximising the Youden index, sensitivity and specificity are considered equally important; this is rarely the case in medicine.”

In the paper

“The fi rst four performance domains (appendix p 2) focus on different aspects of statistical performance, whereas the clinical utility domain focuses on decision-analytical performance.”

In the paper

“Improper measures might mislead researchers instead of clarifying the performance of a model.”

In the paper

“These measures are improper at clinically relevant decision thresholds; in addition, some measures are hard to interpret.”

In the paper

“Displaying the distribution of the risk estimates for each outcome category provides valuable insights into a model's behaviour.”

In the paper

“Remarkably, F1 is the only measure violating both characteristics.”

In the paper

“Net benefit and standardised net benefit are semi-proper; the probability estimates below the threshold can be anything as long as they are below the threshold, and the same goes for probability estimates above the threshold.”

What the sources say

• Not checked yetcites [48] Pepe, 2015, The Net Reclassification Index (NRI): a misleading measure of prediction improvement even with independent test data sets, Stat Biosci source

In the paper

“All discussed overall measures have a focus on statistical performance.”

In the paper

“Discrimination and calibration aid the modeller and clinician to understand how a model can be improved.”

In the paper

“These plots provide limited additional information over AUROC.”

In the paper

“Expected cost is semi-proper because it is insensitive to rank-preserving transformations of the probabilities.”

In the paper

“Standardised net benefit equals net benefit divided by prevalence, and its maximum value is 1.”

What the sources say

• Not checked yetcites [84] Kerr, 2016, Assessing the clinical impact of risk prediction models with decision curves: guidance for correct interpretation and appropriate use, J Clin Oncol source

In the paper

“These measures are hard to interpret and provide a partial assessment of calibration; during internal validation, calibration slope can be used to gauge overfitting.”

What the sources say

• Not checked yetcites [66] Kattan, 2018, The index of prediction accuracy: an intuitive measure useful for evaluating risk prediction models, Diagn Progn Res source

In the paper

“A limitation of these plots is that the thresholds are not easily visible (figure 1).”

What the sources say

• Not checked yetcites [38] Verbakel, 2020, ROC curves for clinical prediction models part 1. ROC plots showed no added value above the AUC when evaluating the performance of clinical prediction models, J Clin Epidemiol source

In the paper

“However, these measures are largely theoretical as they condition on the predicted outcome.”

In the paper

“Setting misclassification costs is not straightforward, and disagreements can occur about what the costs should be (appendix p 13).”

What the sources say

• Not checked yetcites [85] Vickers, 2019, A simple, step-by-step guide to interpreting decision curve analysis, Diagn Progn Res source

In the paper

“These measures are improper; ie, values can be better for incorrect models than for the correct model.”

In the paper

“This measure quantifies discrimination, which is a key component of statistical model performance.”

In the paper

“Net benefit sets the decision threshold based on the misclassification costs, following the classic connection between both.”

What the sources say

• Not checked yetcites [18] Pauker, 1975, Therapeutic decision making: a cost-benefit analysis, N Engl J Med source

In the paper

“In contrast to net benefit, expected cost searches for the decision threshold that minimises cost given the misclassification costs.”

What the sources say

• Not checked yetcites [86] Margineantu, 2000, Bootstrap methods for the cost-sensitive evaluation of classifiers
• Not checked yetcites [87] Ferrer, 2022, Analysis and comparison of classification metrics, arXiv
• Not checked yetcites [88] Provost, 2001, Robust classification for imprecise environments, Mach Learn source
• Not checked yetcites [89] Van Calster, 2015, Calibration of risk prediction models: impact on decision-analytic performance, Med Decis Making source

In the paper

“Poor discrimination indicates that other predictors facilitating improved distinction between individuals with and without the event could be selected.”

In the paper

“Miscalibration of the model might thus be reflected in the decision threshold at which expected cost is minimised, whereas net benefit fi xes the threshold such that miscalibration reduces the net benefit value.”

What the sources say

• Not checked yetcites [89] Van Calster, 2015, Calibration of risk prediction models: impact on decision-analytic performance, Med Decis Making source

In the paper

“These measures attempt to move beyond a statistical assessment but violate decision-analytical principles.”

In the paper

“These measures summarise calibration plots, concealing the nature and direction of miscalibration, and struggle with statistical consistency.”

In the paper

“This measure is interpretable but provides only a partial assessment of calibration; O:E ratio is often 1 or close to 1 during internal validation.”

In the paper

“Similar to F1, MCC has no intuitive interpretation.”

In the paper

“PPV and NPV are highly practical measures because they condition on the classification.”

In the paper

“Overall performance measures combine discrimination and calibration performance, making them less informative than separate assessments of discrimination and calibration performance.”

In the paper

“These measures are improper when used alone.”

In the paper

“NB or standardised NB (with a decision curve) and EC (with a cost curve) Recommended Important measures to quantify to what extent better decisions are made.”

In the paper

“Class imbalance is related to the target population as an epidemiological feature of the data, whereas misclassification costs are clinical concepts that relate to the context of decision making.”

In the paper

“Nevertheless, the principles also hold for other types of outcomes, such as nominal, ordinal, time-to-event, or competing risk outcomes.”

In the paper

“we would expect an O:E ratio close to 1 for welldeveloped models.”

In the paper

“Although competing models can be evaluated using the same core set of measures and visualisations, proper overall measures become more interesting for tasks such as model selection and comparison.”

In the paper

“Decision curves of NB allow one to show potential clinical utility at various clinically relevant decision thresholds relative to default decisions (and competing models).”

In the paper

“First, adequate sample size is important to evaluate performance with sufficient precision.”

In the paper

“Previous recommendations were to include at least 100 to 200 individuals in the smallest outcome category.”

What the sources say

• Not checked yetcites [52] Van Calster, 2016, A calibration hierarchy for risk models was defined: from utopia to empirical data, J Clin Epidemiol source
• Not checked yetcites [99] Collins, 2016, Sample size considerations for the external validation of a multivariable prognostic model: a resampling study, Stat Med source

In the paper

“Miscalibration is often not just a problem of the model but a sign that we need to improve our understanding of the various contexts in which the model is validated and used.”

What the sources say

• Not checked yetcites [91] Van Calster, 2023, There is no such thing as a validated prediction model, BMC Med source

In the paper

“Although competing models can be evaluated using the same core set of measures and visualisations, proper overall measures become more interesting for tasks such as model selection and comparison.”