Risk factors for in-hospital mortality and discharge identified by competing risks multivariate analysis in the derivation set were used to generate a prediction rule. The probability of dying or of being discharged within 40 days after hospital admission was computed for a hypothetical patient identified by a combination of prognostic factors. The prediction accuracy of the fitted models was assessed by discrimination and calibration both in the derivation (internal validation) and validation cohorts (external validation) [7]. Discrimination of the models was assessed by the area under the receiver operating characteristic curve (AUC or C-index) [8]. Calibration was evaluated by comparing the predicted probability with the observed probability at a certain time point by a calibration plot. Finally, the Brier score, which takes into account both the discrimination and the calibration at the same time, was also calculated. It is defined as the expected squared distance between the observed status at that time and the predicted probability [9]. Thus, a smaller value of the Brier score indicates a better model.

To assess the internal validity of the prediction rule, the derivation set was randomly split into a training set (70%) and a test set (30%) [10]. The external validation of the prediction rule was carried out with data from an external validation cohort, represented by the Rome unit, in terms of discrimination, calibration and the Brier score.

The prediction rule has been translated into a web-app that is freely available to the public (COVID-CALC: https://sites.google.com/community.unipa.it/covid-19riskpredictions/c19-rp). (S1 Fig).

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