The decision curve plots the net benefit ( N B ) of a risk model for making decisions over a range of risk thresholds, corresponding to different ratios of misclassification costs. We discuss three methods to estimate the decision curve, together with corresponding methods of inference and methods to compare two risk models at a given risk threshold. One method uses risks (R) and a binary event indicator (Y) on the entire validation cohort. This method makes no assumptions on how well-calibrated the risk model is nor on the incidence of disease in the population and is comparatively robust to model miscalibration. If one assumes that the model is well-calibrated, one can compute a much more precise estimate of N B based on risks R alone. However, if the risk model is miscalibrated, serious bias can result. Case-control data can also be used to estimate N B if the incidence (or prevalence) of the event ( Y = 1 ) is known. This strategy has comparable efficiency to using the full ( R , Y ) data, and its efficiency is only modestly less than that for the full ( R , Y ) data if the incidence is estimated from the mean of Y. We estimate variances using influence functions and propose a bootstrap procedure to obtain simultaneous confidence bands around the decision curve for a range of thresholds. The influence function approach to estimate variances can also be applied to cohorts derived from complex survey samples instead of simple random samples.

中文翻译：

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从三种研究设计中估计决策曲线及其精度

决策曲线绘制了风险模型的净收益 (NB)，用于在一系列风险阈值上做出决策，对应于不同的错误分类成本比率。我们讨论了三种估计决策曲线的方法，以及相应的推理方法和在给定风险阈值下比较两个风险模型的方法。一种方法在整个验证队列中使用风险 (R) 和二元事件指标 (Y)。该方法不对风险模型的校准程度和人群中的疾病发病率做出任何假设，并且对于模型错误校准相对稳健。如果假设模型经过良好校准，则可以仅根据风险 R 计算更精确的 NB 估计。但是，如果风险模型校准错误，可能会导致严重的偏差。如果事件 (Y = 1) 的发生率（或流行）已知，病例对照数据也可用于估计 NB。该策略与使用完整 (R, Y) 数据的效率相当，如果根据 Y 的平均值估计发生率，则其效率仅略低于完整 (R, Y) 数据的效率。我们使用影响来估计方差函数并提出一个引导程序，以获得一系列阈值的决策曲线周围的同时置信带。估计方差的影响函数方法也可以应用于来自复杂调查样本而不是简单随机样本的群组。如果根据 Y 的平均值估计发生率，则其效率仅略低于完整 (R, Y) 数据的效率。我们使用影响函数估计方差并提出一个引导程序来获得决策曲线周围的同时置信带一系列阈值。估计方差的影响函数方法也可以应用于来自复杂调查样本而不是简单随机样本的群组。如果根据 Y 的平均值估计发生率，则其效率仅略低于完整 (R, Y) 数据的效率。我们使用影响函数估计方差并提出一个引导程序来获得决策曲线周围的同时置信带一系列阈值。估计方差的影响函数方法也可以应用于来自复杂调查样本而不是简单随机样本的群组。