OBJECTIVE To review and critically appraise published and preprint reports of prediction models for diagnosing coronavirus disease 2019 (covid-19) in patients with suspected infection, for prognosis of patients with covid-19, and for detecting people in the general population at increased risk of becoming infected with covid-19 or being admitted to hospital with the disease. DESIGNLiving systematic review and critical appraisal. DATA SOURCESPubMed and Embase through Ovid, Arxiv, medRxiv, and bioRxiv up to 7 April 2020.Cite this as: BMJ 2020;369:m1328 http://dx.

Calculating the sample size required for developing a clinical prediction model Clinical prediction models aim to predict outcomes in individuals, to inform diagnosis or prognosis in healthcare. Hundreds of prediction models are published in the medical literature each year, yet many are developed using a dataset that is too small for the total number of participants or outcome events. This leads to inaccurate predictions and consequently incorrect healthcare decisions for some individuals. In this article, the authors provide guidance on how to calculate the sample size required to develop a clinical prediction model.

On behalf of Topic Group 'Evaluating diagnostic tests and prediction models' of the STRATOS initiative 6

Binary logistic regression is one of the most frequently applied statistical approaches for developing clinical prediction models. Developers of such models often rely on an Events Per Variable criterion (EPV), notably EPV ≥10, to determine the minimal sample size required and the maximum number of candidate predictors that can be examined. We present an extensive simulation study in which we studied the influence of EPV, events fraction, number of candidate predictors, the correlations and distributions of candidate predictor variables, area under the ROC curve, and predictor effects on out-of-sample predictive performance of prediction models. The out-of-sample performance (calibration, discrimination and probability prediction error) of developed prediction models was studied before and after regression shrinkage and variable selection. The results indicate that EPV does not have a strong relation with metrics of predictive performance, and is not an appropriate criterion for (binary) prediction model development studies. We show that out-of-sample predictive performance can better be approximated by considering the number of predictors, the total sample size and the events fraction. We propose that the development of new sample size criteria for prediction models should be based on these three parameters, and provide suggestions for improving sample size determination.

BackgroundTen events per variable (EPV) is a widely advocated minimal criterion for sample size considerations in logistic regression analysis. Of three previous simulation studies that examined this minimal EPV criterion only one supports the use of a minimum of 10 EPV. In this paper, we examine the reasons for substantial differences between these extensive simulation studies.MethodsThe current study uses Monte Carlo simulations to evaluate small sample bias, coverage of confidence intervals and mean square error of logit coefficients. Logistic regression models fitted by maximum likelihood and a modified estimation procedure, known as Firth’s correction, are compared.ResultsThe results show that besides EPV, the problems associated with low EPV depend on other factors such as the total sample size. It is also demonstrated that simulation results can be dominated by even a few simulated data sets for which the prediction of the outcome by the covariates is perfect (‘separation’). We reveal that different approaches for identifying and handling separation leads to substantially different simulation results. We further show that Firth’s correction can be used to improve the accuracy of regression coefficients and alleviate the problems associated with separation.ConclusionsThe current evidence supporting EPV rules for binary logistic regression is weak. Given our findings, there is an urgent need for new research to provide guidance for supporting sample size considerations for binary logistic regression analysis.

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.

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BackgroundThe number of proposed prognostic models for COVID-19 is growing rapidly, but it is unknown whether any are suitable for widespread clinical implementation.MethodsWe independently externally validated the performance candidate prognostic models, identified through a living systematic review, among consecutive adults admitted to hospital with a final diagnosis of COVID-19. We reconstructed candidate models as per original descriptions and evaluated performance for their original intended outcomes using predictors measured at admission. We assessed discrimination, calibration and net benefit, compared to the default strategies of treating all and no patients, and against the most discriminating predictor in univariable analyses.ResultsWe tested 22 candidate prognostic models among 411 participants with COVID-19, of whom 180 (43.8%) and 115 (28.0%) met the endpoints of clinical deterioration and mortality, respectively. Highest areas under receiver operating characteristic (AUROC) curves were achieved by the NEWS2 score for prediction of deterioration over 24 h (0.78; 95% CI 0.73–0.83), and a novel model for prediction of deterioration <14 days from admission (0.78; 0.74–0.82). The most discriminating univariable predictors were admission oxygen saturation on room air for in-hospital deterioration (AUROC 0.76; 0.71–0.81), and age for in-hospital mortality (AUROC 0.76; 0.71–0.81). No prognostic model demonstrated consistently higher net benefit than these univariable predictors, across a range of threshold probabilities.ConclusionsAdmission oxygen saturation on room air and patient age are strong predictors of deterioration and mortality among hospitalised adults with COVID-19, respectively. None of the prognostic models evaluated here offered incremental value for patient stratification to these univariable predictors.