arXiv subjects

Ben Van Calster

Publications and source records attributed to Ben Van Calster.

At least 19 recordsLinked to original sources

arXiv2026

Collapsibility of Performance Metrics in Clinical Predictive AI

Background: Population level assessments of predictive artificial intelligence (AI) can conceal performance disparities across subgroups. Fairness evaluations commonly rely on performance analyses across subgroups. However, some performance metrics are non-collapsible, meaning that the overall population performance value does not equal the weighted average of subgroup specific values. Objective: To examine the collapsibility properties of commonly reported performance metrics in predictive AI, with a focus on the area under the receiver operating characteristic curve (AUC, also known as c-statistic). Methods: We investigate the collapsibility of 15 performance metrics, either by expressing each metric as a linear combination of its stratum specific values or, where non-collapsible, by providing a counterexample inspired by Simpson's paradox as a formal disproof. Results: Five performance metrics (AUC, calibration intercept, calibration slope, expected calibration error, and Nagelkerke R^2) are shown to be non-collapsible, and ten (O:E ratio, logloss, Brier score, accuracy, F1-score, true positive rate, true negative rate, positive predictive value, negative predictive value, and net benefit) are shown to be collapsible. The AUC is shown to be non-collapsible because it decomposes into within- and cross-group AUC terms when subpopulations coexist, such that its overall value may fall outside the range of subgroup specific AUCs. Conclusions: Non-collapsibility of performance metrics has important consequences for reporting, model appraisal, and fairness evaluation. It can generate spurious differences between subgroup and overall performance, which may mislead fairness evaluations. Explicitly acknowledging and reporting the collapsibility properties of performance metrics improves both the interpretability and transparency of fairness assessments.

cs.LG↗

arXiv2026

Efficient Variance Estimation for the Polytomous Discrimination Index

Evaluating diagnostic accuracy for multi-category outcomes remains a significant challenge, primarily due to computational limitations in existing performance metrics. The Polytomous Discrimination Index (PDI) has emerged as an order-agnostic solution suitable for nominal classifications. However, its broader adoption has been constrained by the lack of efficient implementation, especially for its variance estimation, which typically would require computationally intensive bootstrapping procedures. In this work, we address this limitation by proposing a novel asymptotic variance estimator for the PDI. Our method integrates classical $U$-statistic theory with recent advances in combinatorics, offering a scalable and theoretically grounded alternative. To assess the performance of the proposed approach, we conduct extensive simulation studies and observe remarkable gain in computing time. We further apply our method to a real-world brain image analysis where deep neural networks are used as a diagnostic tool. We can efficiently report the accuracy of the neural networks with different depth specifications.

stat.CO↗

arXiv2026

Value-of-Information Analysis for External Validation of Risk Prediction Models in Multicenter Studies and Systematic Reviews

External validation studies have finite sample sizes, creating uncertainty about whether a prediction model's Net Benefit (NB) exceeds default strategies' NB. The expected value of perfect information (EVPI) quantifies consequences of uncertainty. Current EVPI methods focus on single studies, ignoring between-center heterogeneity. We extend EVPI and expected value of partial perfect information (EVPPI) to account for between-cluster heterogeneity in multicenter studies and meta-analyses. We distinguish between the global and local optimal strategy and between observed and unobserved clusters. We define EVPIglobal, EVPIcluster_j, EVPIcluster, and EVPPIcluster,prevalence, implemented in the MetaNB R package, and illustrate them using a systematic review across 36 centers of the ADNEX model for ovarian cancer diagnosis. Assuming one global decision regarding ADNEX adoption, there is no need for further data to confirm ADNEX is superior overall (EVPIglobal 0). Meta-analysis borrows information across observed clusters, resulting in consistent local superiority of ADNEX and nonzero but typically lower EVPIcluster_j than when considering local data alone. There is 0.03 probability default strategies are superior in unobserved centers. Eliminating uncertainty on performance and prevalence in each (EVPIcluster) would gain 1134 net avoided false positives (FP) per year, assuming 350000 tumors annually with 20% malignancies. Determining only local prevalence with certainty (EVPPIcluster, prevalence) would gain net 158 avoided FP per year. EVPI extensions disentangle sources of uncertainty and quantify the need for further validation to determine the global or locally optimal strategy. Considering uncertainty and heterogeneity in clinical utility across clusters is essential to decide whether additional validation studies are warranted.

stat.AP↗

arXiv2025

Clustered Flexible Calibration Plots For Binary Outcomes Using Random Effects Modeling

Evaluation of clinical prediction models across multiple clusters, whether centers or datasets, is becoming increasingly common. A comprehensive evaluation includes an assessment of the agreement between the estimated risks and the observed outcomes, also known as calibration. Calibration is of utmost importance for clinical decision making with prediction models and it may vary between clusters. We present three approaches to take clustering into account when evaluating calibration. (1) Clustered group calibration (CG-C), (2) two-stage meta-analysis calibration (2MA-C) and (3) mixed model calibration (MIX-C) can obtain flexible calibration plots with random effects modelling and providing confidence and prediction intervals. As a case example, we externally validate a model to estimate the risk that an ovarian tumor is malignant in multiple centers (N = 2489). We also conduct a simulation study and synthetic data study generated from a true clustered dataset to evaluate the methods. In the simulation study MIX-C and 2MA-C (splines) gave estimated curves closest to the true overall curve. In the synthetic data study MIX-C produced cluster specific curves closest to the truth. Coverage of the prediction interval across the plot was best for 2MA-C with splines. We recommend using 2MA-C with splines to estimate the overall curve and the 95% PI and MIX-C for the cluster specific curves, especially when sample size per cluster is limited. We provide ready-to-use code to construct summary flexible calibration curves with confidence and prediction intervals to assess heterogeneity in calibration across datasets or centers.

stat.ME↗

arXiv2025

Sequential sample size calculations and learning curves safeguard the robust development of a clinical prediction model for individuals

When prospectively developing a new clinical prediction model (CPM), fixed sample size calculations are typically conducted before data collection based on sensible assumptions. But if the assumptions are inaccurate the actual sample size required to develop a reliable model may be very different. To safeguard against this, adaptive sample size approaches have been proposed, based on sequential evaluation of a models predictive performance. Aim: illustrate and extend sequential sample size calculations for CPM development by (i) proposing stopping rules based on minimising uncertainty (instability) and misclassification of individual-level predictions, and (ii) showcasing how it safeguards against inaccurate fixed sample size calculations. Using the sequential approach repeats the pre-defined model development strategy every time a chosen number (e.g., 100) of participants are recruited and adequately followed up. At each stage, CPM performance is evaluated using bootstrapping, leading to prediction and classification stability statistics and plots, alongside optimism-adjusted measures of calibration and discrimination. Our approach is illustrated for development of acute kidney injury using logistic regression CPMs. The fixed sample size calculation, based on perceived sensible assumptions suggests recruiting 342 patients to minimise overfitting; however, the sequential approach reveals that a much larger sample size of 1100 is required to minimise overfitting (targeting population-level stability). If the stopping rule criteria also target small uncertainty and misclassification probability of individual predictions, the sequential approach suggests an even larger sample size (n=1800). Our sequential sample size approach allows users to dynamically monitor individual-level prediction and classification instability and safeguard against using inaccurate assumptions.

stat.ME↗

arXiv2025

Critical Appraisal of Fairness Metrics in Clinical Predictive AI

Predictive artificial intelligence (AI) offers an opportunity to improve clinical practice and patient outcomes, but risks perpetuating biases if fairness is inadequately addressed. However, the definition of "fairness" remains unclear. We conducted a scoping review to identify and critically appraise fairness metrics for clinical predictive AI. We defined a "fairness metric" as a measure quantifying whether a model discriminates (societally) against individuals or groups defined by sensitive attributes. We searched five databases (2014-2024), screening 820 records, to include 41 studies, and extracted 62 fairness metrics. Metrics were classified by performance-dependency, model output level, and base performance metric, revealing a fragmented landscape with limited clinical validation and overreliance on threshold-dependent measures. Eighteen metrics were explicitly developed for healthcare, including only one clinical utility metric. Our findings highlight conceptual challenges in defining and quantifying fairness and identify gaps in uncertainty quantification, intersectionality, and real-world applicability. Future work should prioritise clinically meaningful metrics.

cs.LG↗

arXiv2025

The fundamental problem of risk prediction for individuals: health AI, uncertainty, and personalized medicine

Background and Objective: Clinical prediction models are commonly evaluated regarding performance for a population, although decisions are made for individuals. The classic view relates uncertainty in risk estimates for individuals to sample size (estimation uncertainty) while other sources are model uncertainty (variability in modeling choices) and applicability uncertainty (variability in measurement procedures and between populations). We aim to illustrate the uncertainty of prediction models in estimating individual risks with an ovarian cancer example. Methods: We used real and synthetic data for ovarian cancer diagnosis to train 59400 models with variations in estimation, model, and applicability uncertainty. We then used these models to estimate the probability of ovarian cancer in a fixed test set of 100 patients and evaluate the variability in individual estimates. Results: We show empirically that estimation uncertainty can be strongly dominated by model uncertainty and applicability uncertainty, even for models that perform well at the population level. Estimation uncertainty decreased considerably with increasing training sample size, whereas model and applicability uncertainty remained large. Conclusion: Individual risk estimates are far more uncertain than often assumed. Model uncertainty and applicability uncertainty usually remain invisible when prediction models or algorithms are based on a single study. Predictive algorithms should inform, not dictate, care and support personalization through clinician-patient interaction.

stat.ME↗

arXiv2025

Comparing methods for handling missing data in electronic health records for dynamic risk prediction of central-line associated bloodstream infection

Electronic health records (EHR) often contain varying levels of missing data. This study compared different imputation strategies to identify the most suitable approach for predicting central line-associated bloodstream infection (CLABSI) in the presence of competing risks using EHR data. We analyzed 30862 catheter episodes at University Hospitals Leuven (2012-2013) to predict 7-day CLABSI risk using a landmark cause-specific supermodel, accounting for competing risks of hospital discharge and death. Imputation methods included simple methods (median/mode, last observation carried forward), multiple imputation, regression-based and mixed-effects models leveraging longitudinal structure, and random forest imputation to capture interactions and non-linearities. Missing indicators were also assessed alone and in combination with other imputation methods. Model performance was evaluated dynamically at daily landmarks up to 14 days post-catheter placement. The missing indicator approach showed the highest discriminative ability, achieving a mean AUROC of up to 0.782 and superior overall performance based on the scaled Brier score. Combining missing indicators with other methods slightly improved performance, with the mixed model approach combined with missing indicators achieving the highest AUROC (0.783) at day 4, and the missForestPredict approach combined with missing indicators yielding the best scaled Brier scores at earlier landmarks. This suggests that in EHR data, the presence or absence of information may hold valuable insights for patient risk prediction. However, the use of missing indicators requires caution, as shifts in EHR data over time can alter missing data patterns, potentially impacting model transportability.

stat.AP↗

arXiv2025

Challenges and recommendations for Electronic Health Records data extraction and preparation for dynamic prediction modelling in hospitalized patients -- a practical guide

Dynamic predictive modelling using electronic health record (EHR) data has gained significant attention in recent years. The reliability and trustworthiness of such models depend heavily on the quality of the underlying data, which is, in part, determined by the stages preceding the model development: data extraction from EHR systems and data preparation. In this article, we identified over forty challenges encountered during these stages and provide actionable recommendations for addressing them. These challenges are organized into four categories: cohort definition, outcome definition, feature engineering, and data cleaning. This comprehensive list serves as a practical guide for data extraction engineers and researchers, promoting best practices and improving the quality and real-world applicability of dynamic prediction models in clinical settings.

cs.LG↗

arXiv2024

Performance evaluation of predictive AI models to support medical decisions: Overview and guidance

A myriad of measures to illustrate performance of predictive artificial intelligence (AI) models have been proposed in the literature. Selecting appropriate performance measures is essential for predictive AI models that are developed to be used in medical practice, because poorly performing models may harm patients and lead to increased costs. We aim to assess the merits of classic and contemporary performance measures when validating predictive AI models for use in medical practice. We focus on models with a binary outcome. We discuss 32 performance measures covering five performance domains (discrimination, calibration, overall, classification, and clinical utility) along with accompanying graphical assessments. The first four domains cover statistical performance, the fifth domain covers decision-analytic performance. We explain why two key characteristics are important when selecting which performance measures to assess: (1) whether the measure's expected value is optimized when it is calculated using the correct probabilities (i.e., a "proper" measure), and (2) whether they reflect either purely statistical performance or decision-analytic performance by properly considering misclassification costs. Seventeen measures exhibit both characteristics, fourteen measures exhibited one characteristic, and one measure possessed neither characteristic (the F1 measure). All classification measures (such as classification accuracy and F1) are improper for clinically relevant decision thresholds other than 0.5 or the prevalence. We recommend the following measures and plots as essential to report: AUROC, calibration plot, a clinical utility measure such as net benefit with decision curve analysis, and a plot with probability distributions per outcome category.

cs.LG↗

arXiv2024

Understanding overfitting in random forest for probability estimation: a visualization and simulation study

Random forests have become popular for clinical risk prediction modelling. In a case study on predicting ovarian malignancy, we observed training c-statistics close to 1. Although this suggests overfitting, performance was competitive on test data. We aimed to understand the behaviour of random forests by (1) visualizing data space in three real world case studies and (2) a simulation study. For the case studies, risk estimates were visualised using heatmaps in a 2-dimensional subspace. The simulation study included 48 logistic data generating mechanisms (DGM), varying the predictor distribution, the number of predictors, the correlation between predictors, the true c-statistic and the strength of true predictors. For each DGM, 1000 training datasets of size 200 or 4000 were simulated and RF models trained with minimum node size 2 or 20 using ranger package, resulting in 192 scenarios in total. The visualizations suggested that the model learned spikes of probability around events in the training set. A cluster of events created a bigger peak, isolated events local peaks. In the simulation study, median training c-statistics were between 0.97 and 1 unless there were 4 or 16 binary predictors with minimum node size 20. Median test c-statistics were higher with higher events per variable, higher minimum node size, and binary predictors. Median training slopes were always above 1, and were not correlated with median test slopes across scenarios (correlation -0.11). Median test slopes were higher with higher true c-statistic, higher minimum node size, and higher sample size. Random forests learn local probability peaks that often yield near perfect training c-statistics without strongly affecting c-statistics on test data. When the aim is probability estimation, the simulation results go against the common recommendation to use fully grown trees in random forest models.

stat.ME↗

arXiv2024

missForestPredict -- Missing data imputation for prediction settings

Prediction models are used to predict an outcome based on input variables. Missing data in input variables often occurs at model development and at prediction time. The missForestPredict R package proposes an adaptation of the missForest imputation algorithm that is fast, user-friendly and tailored for prediction settings. The algorithm iteratively imputes variables using random forests until a convergence criterion (unified for continuous and categorical variables and based on the out-of-bag error) is met. The imputation models are saved for each variable and iteration and can be applied later to new observations at prediction time. The missForestPredict package offers extended error monitoring, control over variables used in the imputation and custom initialization. This allows users to tailor the imputation to their specific needs. The missForestPredict algorithm is compared to mean/mode imputation, linear regression imputation, mice, k-nearest neighbours, bagging, miceRanger and IterativeImputer on eight simulated datasets with simulated missingness (48 scenarios) and eight large public datasets using different prediction models. missForestPredict provides competitive results in prediction settings within short computation times.

stat.ME↗

arXiv2024

Comparison of static and dynamic random forests models for EHR data in the presence of competing risks: predicting central line-associated bloodstream infection

Prognostic outcomes related to hospital admissions typically do not suffer from censoring, and can be modeled either categorically or as time-to-event. Competing events are common but often ignored. We compared the performance of random forest (RF) models to predict the risk of central line-associated bloodstream infections (CLABSI) using different outcome operationalizations. We included data from 27478 admissions to the University Hospitals Leuven, covering 30862 catheter episodes (970 CLABSI, 1466 deaths and 28426 discharges) to build static and dynamic RF models for binary (CLABSI vs no CLABSI), multinomial (CLABSI, discharge, death or no event), survival (time to CLABSI) and competing risks (time to CLABSI, discharge or death) outcomes to predict the 7-day CLABSI risk. We evaluated model performance across 100 train/test splits. Performance of binary, multinomial and competing risks models was similar: AUROC was 0.74 for baseline predictions, rose to 0.78 for predictions at day 5 in the catheter episode, and decreased thereafter. Survival models overestimated the risk of CLABSI (E:O ratios between 1.2 and 1.6), and had AUROCs about 0.01 lower than other models. Binary and multinomial models had lowest computation times. Models including multiple outcome events (multinomial and competing risks) display a different internal structure compared to binary and survival models. In the absence of censoring, complex modelling choices do not considerably improve the predictive performance compared to a binary model for CLABSI prediction in our studied settings. Survival models censoring the competing events at their time of occurrence should be avoided.

cs.LG↗

arXiv2024

A comparison of regression models for static and dynamic prediction of a prognostic outcome during admission in electronic health care records

Objective Hospitals register information in the electronic health records (EHR) continuously until discharge or death. As such, there is no censoring for in-hospital outcomes. We aimed to compare different dynamic regression modeling approaches to predict central line-associated bloodstream infections (CLABSI) in EHR while accounting for competing events precluding CLABSI. Materials and Methods We analyzed data from 30,862 catheter episodes at University Hospitals Leuven from 2012 and 2013 to predict 7-day risk of CLABSI. Competing events are discharge and death. Static models at catheter onset included logistic, multinomial logistic, Cox, cause-specific hazard, and Fine-Gray regression. Dynamic models updated predictions daily up to 30 days after catheter onset (i.e. landmarks 0 to 30 days), and included landmark supermodel extensions of the static models, separate Fine-Gray models per landmark time, and regularized multi-task learning (RMTL). Model performance was assessed using 100 random 2:1 train-test splits. Results The Cox model performed worst of all static models in terms of area under the receiver operating characteristic curve (AUC) and calibration. Dynamic landmark supermodels reached peak AUCs between 0.741-0.747 at landmark 5. The Cox landmark supermodel had the worst AUCs (<=0.731) and calibration up to landmark 7. Separate Fine-Gray models per landmark performed worst for later landmarks, when the number of patients at risk was low. Discussion and Conclusion Categorical and time-to-event approaches had similar performance in the static and dynamic settings, except Cox models. Ignoring competing risks caused problems for risk prediction in the time-to-event framework (Cox), but not in the categorical framework (logistic regression).

stat.AP↗

arXiv2024

Understanding metric-related pitfalls in image analysis validation

Validation metrics are key for the reliable tracking of scientific progress and for bridging the current chasm between artificial intelligence (AI) research and its translation into practice. However, increasing evidence shows that particularly in image analysis, metrics are often chosen inadequately in relation to the underlying research problem. This could be attributed to a lack of accessibility of metric-related knowledge: While taking into account the individual strengths, weaknesses, and limitations of validation metrics is a critical prerequisite to making educated choices, the relevant knowledge is currently scattered and poorly accessible to individual researchers. Based on a multi-stage Delphi process conducted by a multidisciplinary expert consortium as well as extensive community feedback, the present work provides the first reliable and comprehensive common point of access to information on pitfalls related to validation metrics in image analysis. Focusing on biomedical image analysis but with the potential of transfer to other fields, the addressed pitfalls generalize across application domains and are categorized according to a newly created, domain-agnostic taxonomy. To facilitate comprehension, illustrations and specific examples accompany each pitfall. As a structured body of information accessible to researchers of all levels of expertise, this work enhances global comprehension of a key topic in image analysis validation.

cs.CV↗

arXiv2024

Metrics reloaded: Recommendations for image analysis validation

Increasing evidence shows that flaws in machine learning (ML) algorithm validation are an underestimated global problem. Particularly in automatic biomedical image analysis, chosen performance metrics often do not reflect the domain interest, thus failing to adequately measure scientific progress and hindering translation of ML techniques into practice. To overcome this, our large international expert consortium created Metrics Reloaded, a comprehensive framework guiding researchers in the problem-aware selection of metrics. Following the convergence of ML methodology across application domains, Metrics Reloaded fosters the convergence of validation methodology. The framework was developed in a multi-stage Delphi process and is based on the novel concept of a problem fingerprint - a structured representation of the given problem that captures all aspects that are relevant for metric selection, from the domain interest to the properties of the target structure(s), data set and algorithm output. Based on the problem fingerprint, users are guided through the process of choosing and applying appropriate validation metrics while being made aware of potential pitfalls. Metrics Reloaded targets image analysis problems that can be interpreted as a classification task at image, object or pixel level, namely image-level classification, object detection, semantic segmentation, and instance segmentation tasks. To improve the user experience, we implemented the framework in the Metrics Reloaded online tool, which also provides a point of access to explore weaknesses, strengths and specific recommendations for the most common validation metrics. The broad applicability of our framework across domains is demonstrated by an instantiation for various biological and medical image analysis use cases.

cs.CV↗

arXiv2023

How to develop, externally validate, and update multinomial prediction models

Multinomial prediction models (MPMs) have a range of potential applications across healthcare where the primary outcome of interest has multiple nominal or ordinal categories. However, the application of MPMs is scarce, which may be due to the added methodological complexities that they bring. This article provides a guide of how to develop, externally validate, and update MPMs. Using a previously developed and validated MPM for treatment outcomes in rheumatoid arthritis as an example, we outline guidance and recommendations for producing a clinical prediction model using multinomial logistic regression. This article is intended to supplement existing general guidance on prediction model research. This guide is split into three parts: 1) Outcome definition and variable selection, 2) Model development, and 3) Model evaluation (including performance assessment, internal and external validation, and model recalibration). We outline how to evaluate and interpret the predictive performance of MPMs. R code is provided. We recommend the application of MPMs in clinical settings where the prediction of a nominal polytomous outcome is of interest. Future methodological research could focus on MPM-specific considerations for variable selection and sample size criteria for external validation.

stat.ME↗

arXiv2023

Common Limitations of Image Processing Metrics: A Picture Story

While the importance of automatic image analysis is continuously increasing, recent meta-research revealed major flaws with respect to algorithm validation. Performance metrics are particularly key for meaningful, objective, and transparent performance assessment and validation of the used automatic algorithms, but relatively little attention has been given to the practical pitfalls when using specific metrics for a given image analysis task. These are typically related to (1) the disregard of inherent metric properties, such as the behaviour in the presence of class imbalance or small target structures, (2) the disregard of inherent data set properties, such as the non-independence of the test cases, and (3) the disregard of the actual biomedical domain interest that the metrics should reflect. This living dynamically document has the purpose to illustrate important limitations of performance metrics commonly applied in the field of image analysis. In this context, it focuses on biomedical image analysis problems that can be phrased as image-level classification, semantic segmentation, instance segmentation, or object detection task. The current version is based on a Delphi process on metrics conducted by an international consortium of image analysis experts from more than 60 institutions worldwide.

eess.IV↗