Equivalence of binormal likelihood-ratio and bi-chi-squared ROC curve models.
Equivalence of binormal likelihood-ratio and bi-chi-squared ROC curve models.
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二手型可能比率和双chi方方曲线曲线模型的等效性。
DOI：
10.1002/sim.6816
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发表时间：
2016-05-30
影响因子：
2
通讯作者：
Hillis SL
中科院分区：
文献类型：
--
作者：
Hillis SL
有意义的诊断决策变量的一个基本假设是，它和它的似然比之间存在单调关系。然而，这种关系通常不适用于导致二次正态ROC曲线的决策变量。因此，基于双正态ROC曲线模型的假设的接收者操作特征(ROC)曲线估计会产生不正确的ROC曲线，这些ROC曲线具有“钩子”，在整个域上不是凹的，并且跨越机会线。虽然在实践中这种“不恰当”通常是不明显的，但有时它是明显的和有问题的。为了避免这个问题，Metz和潘提出了基于双正态似然比模型的ROC曲线估计，该模型规定决策变量是具有正态条件病态和非病态分布的随机变量的似然比函数的递增变换。然而，它们的发展并不容易效仿。在相应的ROC曲线族相同的意义下，证明了Binormal-LR模型等价于双X平方模型。比卡方公式提供了一种更容易跟踪的Binormal-LR ROC曲线的发展及其在众所周知的分布方面的性质。
A basic assumption for a meaningful diagnostic decision variable is that there is a monotone relationship between it and its likelihood ratio. This relationship, however, generally does not hold for a decision variable that results in a binormal ROC curve. As a result, receiver operating characteristic (ROC) curve estimation based on the assumption of a binormal ROC-curve model produces improper ROC curves that have “hooks,” are not concave over the entire domain, and cross the chance line. Although in practice this “improperness” is usually not noticeable, sometimes it is evident and problematic. To avoid this problem, Metz and Pan proposed basing ROC-curve estimation on the assumption of a binormal likelihood-ratio (binormal-LR) model, which states that the decision variable is an increasing transformation of the likelihood-ratio function of a random variable having normal conditional diseased and nondiseased distributions. However, their development is not easy to follow. I show that the binormal-LR model is equivalent to a bi-chi-squared model in the sense that the families of corresponding ROC curves are the same. The bi-chi-squared formulation provides an easier-to-follow development of the binormal-LR ROC curve and its properties in terms of well-known distributions.
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