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The performance of risk prediction models is often characterized in terms ofdiscrimination and calibration. The Receiver Operating Characteristic (ROC)curve is widely used for evaluating model discrimination. When evaluating theperformance of a risk prediction model in a new sample, the shape of the ROCcurve is affected by both case-mix and the postulated model. Further, comparedto discrimination, evaluating calibration has not received the same level ofattention. Commonly used methods for model calibration involve subjectivespecification of smoothing or grouping. Leveraging the familiar ROC framework,we introduce the model-based ROC (mROC) curve to assess the calibration of apre-specified model in a new sample. mROC curve is the ROC curve that should beobserved if a pre-specified model is calibrated in the sample. We show theempirical ROC and mROC curves for a sample converge asymptotically if the modelis calibrated in that sample. As a consequence, the mROC curve can be used toassess visually the effect of case-mix and model mis-calibration. Further, wepropose a novel statistical test for calibration that does not require anysmoothing or grouping. Simulations support the adequacy of the test. A casestudy puts these developments in a practical context. We conclude that mROC caneasily be constructed and used to evaluate the effect of case-mix and modelcalibration on the ROC plot, thus adding to the utility of ROC curve analysisin the evaluation of risk prediction models. R code for the proposedmethodology is provided (https://github.com/msadatsafavi/mROC/).

Model-based ROC (mROC) curve: examining the effect of case-mix and model calibration on the ROC plot