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Evaluating the performance of a clinical prediction model is crucial to establish its predictive accuracy in the populations and settings intended for use. In this article, the first in a three part series, Collins and colleagues describe the importance of a meaningful evaluation using internal, internal-external, and external validation, as well as exploring heterogeneity, fairness, and generalisability in model performance.

IntroductionThe Transparent Reporting of a multivariable prediction model of Individual Prognosis Or Diagnosis (TRIPOD) statement and the Prediction model Risk Of Bias ASsessment Tool (PROBAST) were both published to improve the reporting and critical appraisal of prediction model studies for diagnosis and prognosis. This paper describes the processes and methods that will be used to develop an extension to the TRIPOD statement (TRIPOD-artificial intelligence, AI) and the PROBAST (PROBAST-AI) tool for prediction model studies that applied machine learning techniques.Methods and analysisTRIPOD-AI and PROBAST-AI will be developed following published guidance from the EQUATOR Network, and will comprise five stages. Stage 1 will comprise two systematic reviews (across all medical fields and specifically in oncology) to examine the quality of reporting in published machine-learning-based prediction model studies. In stage 2, we will consult a diverse group of key stakeholders using a Delphi process to identify items to be considered for inclusion in TRIPOD-AI and PROBAST-AI. Stage 3 will be virtual consensus meetings to consolidate and prioritise key items to be included in TRIPOD-AI and PROBAST-AI. Stage 4 will involve developing the TRIPOD-AI checklist and the PROBAST-AI tool, and writing the accompanying explanation and elaboration papers. In the final stage, stage 5, we will disseminate TRIPOD-AI and PROBAST-AI via journals, conferences, blogs, websites (including TRIPOD, PROBAST and EQUATOR Network) and social media. TRIPOD-AI will provide researchers working on prediction model studies based on machine learning with a reporting guideline that can help them report key details that readers need to evaluate the study quality and interpret its findings, potentially reducing research waste. We anticipate PROBAST-AI will help researchers, clinicians, systematic reviewers and policymakers critically appraise the design, conduct and analysis of machine learning based prediction model studies, with a robust standardised tool for bias evaluation.Ethics and disseminationEthical approval has been granted by the Central University Research Ethics Committee, University of Oxford on 10-December-2020 (R73034/RE001). Findings from this study will be disseminated through peer-review publications.PROSPERO registration numberCRD42019140361 and CRD42019161764.

AbstractObjectiveTo review and appraise the validity and usefulness of published and preprint reports of prediction models for prognosis of patients with covid-19, and for detecting people in the general population at increased risk of covid-19 infection or being admitted to hospital or dying with the disease.DesignLiving systematic review and critical appraisal by the covid-PRECISE (Precise Risk Estimation to optimise covid-19 Care for Infected or Suspected patients in diverse sEttings) group.Data sourcesPubMed and Embase through Ovid, up to 17 February 2021, supplemented with arXiv, medRxiv, and bioRxiv up to 5 May 2020.Study selectionStudies that developed or validated a multivariable covid-19 related prediction model.Data extractionAt least two authors independently extracted data using the CHARMS (critical appraisal and data extraction for systematic reviews of prediction modelling studies) checklist; risk of bias was assessed using PROBAST (prediction model risk of bias assessment tool).Results126 978 titles were screened, and 412 studies describing 731 new prediction models or validations were included. Of these 731, 125 were diagnostic models (including 75 based on medical imaging) and the remaining 606 were prognostic models for either identifying those at risk of covid-19 in the general population (13 models) or predicting diverse outcomes in those individuals with confirmed covid-19 (593 models). Owing to the widespread availability of diagnostic testing capacity after the summer of 2020, this living review has now focused on the prognostic models. Of these, 29 had low risk of bias, 32 had unclear risk of bias, and 545 had high risk of bias. The most common causes for high risk of bias were inadequate sample sizes (n=408, 67%) and inappropriate or incomplete evaluation of model performance (n=338, 56%). 381 models were newly developed, and 225 were external validations of existing models. The reported C indexes varied between 0.77 and 0.93 in development studies with low risk of bias, and between 0.56 and 0.78 in external validations with low risk of bias. The Qcovid models, the PRIEST score, Carr’s model, the ISARIC4C Deterioration model, and the Xie model showed adequate predictive performance in studies at low risk of bias. Details on all reviewed models are publicly available at https://www.covprecise.org/.ConclusionPrediction models for covid-19 entered the academic literature to support medical decision making at unprecedented speed and in large numbers. Most published prediction model studies were poorly reported and at high risk of bias such that their reported predictive performances are probably optimistic. Models with low risk of bias should be validated before clinical implementation, preferably through collaborative efforts to also allow an investigation of the heterogeneity in their performance across various populations and settings. Methodological guidance, as provided in this paper, should be followed because unreliable predictions could cause more harm than benefit in guiding clinical decisions. Finally, prediction modellers should adhere to the TRIPOD (transparent reporting of a multivariable prediction model for individual prognosis or diagnosis) reporting guideline.Systematic review registrationProtocol https://osf.io/ehc47/, registration https://osf.io/wy245.Readers’ noteThis article is the final version of a living systematic review that has been updated over the past two years to reflect emerging evidence. This version is update 4 of the original article published on 7 April 2020 (BMJ 2020;369:m1328). Previous updates can be found as data supplements (https://www.bmj.com/content/369/bmj.m1328/related#datasupp). When citing this paper please consider adding the update number and date of access for clarity.

Background Random forests have become popular for clinical risk prediction modeling. In a case study on predicting ovarian malignancy, we observed training AUCs close to 1. Although this suggests overfitting, performance was competitive on test data. We aimed to understand the behavior of random forests for probability estimation by (1) visualizing data space in three real-world case studies and (2) a simulation study. Methods For the case studies, multinomial risk estimates were visualized 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 AUC, and the strength of true predictors. For each DGM, 1000 training datasets of size 200 or 4000 with binary outcomes were simulated, and random forest models were trained with minimum node size 2 or 20 using the ranger R package, resulting in 192 scenarios in total. Model performance was evaluated on large test datasets ( N  = 100,000). Results The visualizations suggested that the model learned “spikes of probability” around events in the training set. A cluster of events created a bigger peak or plateau (signal), isolated events local peaks (noise). In the simulation study, median training AUCs were between 0.97 and 1 unless there were 4 binary predictors or 16 binary predictors with a minimum node size of 20. The median discrimination loss, i.e., the difference between the median test AUC and the true AUC, was 0.025 (range 0.00 to 0.13). Median training AUCs had Spearman correlations of around 0.70 with discrimination loss. Median test AUCs were higher with higher events per variable, higher minimum node size, and binary predictors. Median training calibration slopes were always above 1 and were not correlated with median test slopes across scenarios (Spearman correlation − 0.11). Median test slopes were higher with higher true AUC, higher minimum node size, and higher sample size. Conclusions Random forests learn local probability peaks that often yield near perfect training AUCs without strongly affecting AUCs 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.

When developing a clinical prediction model, assuming a linear relationship between the continuous predictors and outcome is not recommended. Incorrect specification of the functional form of continuous predictors could reduce predictive accuracy. We examine how continuous predictors are handled in studies developing a clinical prediction model. We searched PubMed for clinical prediction model studies developing a logistic regression model for a binary outcome, published between July 01, 2020, and July 30, 2020. In total, 118 studies were included in the review (18 studies (15%) assessed the linearity assumption or used methods to handle nonlinearity, and 100 studies (85%) did not). Transformation and splines were commonly used to handle nonlinearity, used in 7 (n = 7/18, 39%) and 6 (n = 6/18, 33%) studies, respectively. Categorization was most often used method to handle continuous predictors (n = 67/118, 56.8%) where most studies used dichotomization (n = 40/67, 60%). Only ten models included nonlinear terms in the final model (n = 10/18, 56%). Though widely recommended not to categorize continuous predictors or assume a linear relationship between outcome and continuous predictors, most studies categorize continuous predictors, few studies assess the linearity assumption, and even fewer use methodology to account for nonlinearity. Methodological guidance is provided to guide researchers on how to handle continuous predictors when developing a clinical prediction model.

Background Each year, thousands of clinical prediction models are developed to make predictions (e.g. estimated risk) to inform individual diagnosis and prognosis in healthcare. However, most are not reliable for use in clinical practice. Main body We discuss how the creation of a prediction model (e.g. using regression or machine learning methods) is dependent on the sample and size of data used to develop it—were a different sample of the same size used from the same overarching population, the developed model could be very different even when the same model development methods are used. In other words, for each model created, there exists a multiverse of other potential models for that sample size and, crucially, an individual’s predicted value (e.g. estimated risk) may vary greatly across this multiverse. The more an individual’s prediction varies across the multiverse, the greater the instability. We show how small development datasets lead to more different models in the multiverse, often with vastly unstable individual predictions, and explain how this can be exposed by using bootstrapping and presenting instability plots. We recommend healthcare researchers seek to use large model development datasets to reduce instability concerns. This is especially important to ensure reliability across subgroups and improve model fairness in practice. Conclusions Instability is concerning as an individual’s predicted value is used to guide their counselling, resource prioritisation, and clinical decision making. If different samples lead to different models with very different predictions for the same individual, then this should cast doubt into using a particular model for that individual. Therefore, visualising, quantifying and reporting the instability in individual-level predictions is essential when proposing a new model.

Background Having an appropriate sample size is important when developing a clinical prediction model. We aimed to review how sample size is considered in studies developing a prediction model for a binary outcome. Methods We searched PubMed for studies published between 01/07/2020 and 30/07/2020 and reviewed the sample size calculations used to develop the prediction models. Using the available information, we calculated the minimum sample size that would be needed to estimate overall risk and minimise overfitting in each study and summarised the difference between the calculated and used sample size. Results A total of 119 studies were included, of which nine studies provided sample size justification (8%). The recommended minimum sample size could be calculated for 94 studies: 73% (95% CI: 63–82%) used sample sizes lower than required to estimate overall risk and minimise overfitting including 26% studies that used sample sizes lower than required to estimate overall risk only. A similar number of studies did not meet the ≥ 10EPV criteria (75%, 95% CI: 66–84%). The median deficit of the number of events used to develop a model was 75 [IQR: 234 lower to 7 higher]) which reduced to 63 if the total available data (before any data splitting) was used [IQR:225 lower to 7 higher]. Studies that met the minimum required sample size had a median c-statistic of 0.84 (IQR:0.80 to 0.9) and studies where the minimum sample size was not met had a median c-statistic of 0.83 (IQR: 0.75 to 0.9). Studies that met the ≥ 10 EPP criteria had a median c-statistic of 0.80 (IQR: 0.73 to 0.84). Conclusions Prediction models are often developed with no sample size calculation, as a consequence many are too small to precisely estimate the overall risk. We encourage researchers to justify, perform and report sample size calculations when developing a prediction model.

Background Describe and evaluate the methodological conduct of prognostic prediction models developed using machine learning methods in oncology. Methods We conducted a systematic review in MEDLINE and Embase between 01/01/2019 and 05/09/2019, for studies developing a prognostic prediction model using machine learning methods in oncology. We used the Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis (TRIPOD) statement, Prediction model Risk Of Bias ASsessment Tool (PROBAST) and CHecklist for critical Appraisal and data extraction for systematic Reviews of prediction Modelling Studies (CHARMS) to assess the methodological conduct of included publications. Results were summarised by modelling type: regression-, non-regression-based and ensemble machine learning models. Results Sixty-two publications met inclusion criteria developing 152 models across all publications. Forty-two models were regression-based, 71 were non-regression-based and 39 were ensemble models. A median of 647 individuals (IQR: 203 to 4059) and 195 events (IQR: 38 to 1269) were used for model development, and 553 individuals (IQR: 69 to 3069) and 50 events (IQR: 17.5 to 326.5) for model validation. A higher number of events per predictor was used for developing regression-based models (median: 8, IQR: 7.1 to 23.5), compared to alternative machine learning (median: 3.4, IQR: 1.1 to 19.1) and ensemble models (median: 1.7, IQR: 1.1 to 6). Sample size was rarely justified ( n  = 5/62; 8%). Some or all continuous predictors were categorised before modelling in 24 studies (39%). 46% ( n  = 24/62) of models reporting predictor selection before modelling used univariable analyses, and common method across all modelling types. Ten out of 24 models for time-to-event outcomes accounted for censoring (42%). A split sample approach was the most popular method for internal validation ( n  = 25/62, 40%). Calibration was reported in 11 studies. Less than half of models were reported or made available. Conclusions The methodological conduct of machine learning based clinical prediction models is poor. Guidance is urgently needed, with increased awareness and education of minimum prediction modelling standards. Particular focus is needed on sample size estimation, development and validation analysis methods, and ensuring the model is available for independent validation, to improve quality of machine learning based clinical prediction models.

Background While many studies have consistently found incomplete reporting of regression-based prediction model studies, evidence is lacking for machine learning-based prediction model studies. We aim to systematically review the adherence of Machine Learning (ML)-based prediction model studies to the Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis (TRIPOD) Statement. Methods We included articles reporting on development or external validation of a multivariable prediction model (either diagnostic or prognostic) developed using supervised ML for individualized predictions across all medical fields. We searched PubMed from 1 January 2018 to 31 December 2019. Data extraction was performed using the 22-item checklist for reporting of prediction model studies ( www.TRIPOD-statement.org ). We measured the overall adherence per article and per TRIPOD item. Results Our search identified 24,814 articles, of which 152 articles were included: 94 (61.8%) prognostic and 58 (38.2%) diagnostic prediction model studies. Overall, articles adhered to a median of 38.7% (IQR 31.0–46.4%) of TRIPOD items. No article fully adhered to complete reporting of the abstract and very few reported the flow of participants (3.9%, 95% CI 1.8 to 8.3), appropriate title (4.6%, 95% CI 2.2 to 9.2), blinding of predictors (4.6%, 95% CI 2.2 to 9.2), model specification (5.2%, 95% CI 2.4 to 10.8), and model’s predictive performance (5.9%, 95% CI 3.1 to 10.9). There was often complete reporting of source of data (98.0%, 95% CI 94.4 to 99.3) and interpretation of the results (94.7%, 95% CI 90.0 to 97.3). Conclusion Similar to prediction model studies developed using conventional regression-based techniques, the completeness of reporting is poor. Essential information to decide to use the model (i.e. model specification and its performance) is rarely reported. However, some items and sub-items of TRIPOD might be less suitable for ML-based prediction model studies and thus, TRIPOD requires extensions. Overall, there is an urgent need to improve the reporting quality and usability of research to avoid research waste. Systematic review registration PROSPERO, CRD42019161764.

Clinical prediction models estimate an individual’s risk (probability) of a health related outcome to help guide patient counselling and clinical decision making. Most models provide a single point estimate of risk but without the associated uncertainty. Riley and colleagues argue that this needs to change, as understanding uncertainty of risk estimates helps to inform critical evaluation of a model and may impact shared decision making. Examples are provided to illustrate uncertainty in risk estimates, and key methods to quantify and present uncertainty are discussed.