基于模型的ROC（mROC）曲线：检查病例组合和模型校准对ROC图的影响
Model-based ROC (mROC) curve: examining the effect of case-mix and model calibration on the ROC plot
摘要：
风险预测模型的性能通常以区分和校准为特征。受试者工作特征（ROC）曲线被广泛用于评估模型区分度。当评估风险预测模型在新样本中的性能时，ROC曲线的形状受到病例组合和假设模型的影响。此外，与辨别力相比，评价校准没有得到同等程度的关注。常用的模型校准方法涉及平滑或分组的主观规范。利用熟悉的ROC框架，我们引入了基于模型的ROC（mROC）曲线来评估新样本中预先指定的模型的校准。mROC曲线是在样本中校准预先指定的模型时应观察到的ROC曲线。我们表明，如果模型在该样本中进行校准，则样本的经验ROC和mROC曲线渐近收敛。因此，mROC曲线可用于直观评估病例组合和模型误校准的影响。此外，我们提出了一种新的统计测试校准，不需要任何平滑或分组。模拟支持测试的充分性。一项案例研究将这些发展置于实际背景下。我们的结论是，mROC可以很容易地构建和使用的情况下，组合和模型校准的ROC图的效果进行评估，从而增加了ROC曲线分析的效用在风险预测模型的评估。提供了用于所提出的方法的R代码（https：//github.com/msadatsafavi/mROC/）。
英文摘要：
The performance of risk prediction models is often characterized in terms of discrimination and calibration. The Receiver Operating Characteristic (ROC) curve is widely used for evaluating model discrimination. When evaluating the performance of a risk prediction model in a new sample, the shape of the ROC curve is affected by both case-mix and the postulated model. Further, compared to discrimination, evaluating calibration has not received the same level of attention. Commonly used methods for model calibration involve subjective specification of smoothing or grouping. Leveraging the familiar ROC framework, we introduce the model-based ROC (mROC) curve to assess the calibration of a pre-specified model in a new sample. mROC curve is the ROC curve that should be observed if a pre-specified model is calibrated in the sample. We show the empirical ROC and mROC curves for a sample converge asymptotically if the model is calibrated in that sample. As a consequence, the mROC curve can be used to assess visually the effect of case-mix and model mis-calibration. Further, we propose a novel statistical test for calibration that does not require any smoothing or grouping. Simulations support the adequacy of the test. A case study puts these developments in a practical context. We conclude that mROC can easily be constructed and used to evaluate the effect of case-mix and model calibration on the ROC plot, thus adding to the utility of ROC curve analysis in the evaluation of risk prediction models. R code for the proposed methodology is provided (https://github.com/msadatsafavi/mROC/).
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