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.

Summary Appropriate quantification of added usefulness offered by new markers included in risk prediction algorithms is a problem of active research and debate. Standard methods, including statistical significance and c statistic are useful but not sufficient. Net reclassification improvement (NRI) offers a simple intuitive way of quantifying improvement offered by new markers and has been gaining popularity among researchers. However, several aspects of the NRI have not been studied in sufficient detail. In this paper we propose a prospective formulation for the NRI which offers immediate application to survival and competing risk data as well as allows for easy weighting with observed or perceived costs. We address the issue of the number and choice of categories and their impact on NRI. We contrast category-based NRI with one which is category-free and conclude that NRIs cannot be compared across studies unless they are defined in the same manner. We discuss the impact of differing event rates when models are applied to different samples or definitions of events and durations of follow-up vary between studies. We also show how NRI can be applied to case-control data. The concepts presented in the paper are illustrated in a Framingham Heart Study example. In conclusion, NRI can be readily calculated for survival, competing risk, and case-control data, is more objective and comparable across studies using the category-free version, and can include relative costs for classifications. We recommend that researchers clearly define and justify the choices they make when choosing NRI for their application.

The performance of prediction models can be assessed using a variety of different methods and metrics. Traditional measures for binary and survival outcomes include the Brier score to indicate overall model performance, the concordance (or c) statistic for discriminative ability (or area under the receiver operating characteristic (ROC) curve), and goodness-of-fit statistics for calibration. Several new measures have recently been proposed that can be seen as refinements of discrimination measures, including variants of the c statistic for survival, reclassification tables, net reclassification improvement (NRI), and integrated discrimination improvement (IDI). Moreover, decision–analytic measures have been proposed, including decision curves to plot the net benefit achieved by making decisions based on model predictions. We aimed to define the role of these relatively novel approaches in the evaluation of the performance of prediction models. For illustration we present a case study of predicting the presence of residual tumor versus benign tissue in patients with testicular cancer (n=544 for model development, n=273 for external validation). We suggest that reporting discrimination and calibration will always be important for a prediction model. Decision-analytic measures should be reported if the predictive model is to be used for making clinical decisions. Other measures of performance may be warranted in specific applications, such as reclassification metrics to gain insight into the value of adding a novel predictor to an established model.