RECEIVER OPERATING CHARACTERISTIC CURVE BASED ON POWER-NORMAL DISTRIBUTION

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  • ベキ正規分布に基づくROC曲線の構成
  • ベキ セイキ ブンプ ニ モトズク ROC キョクセン ノ コウセイ

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Abstract

In medical science, it is one of important subjects to explore the diagnostic test based on which we can discriminate the disease and non-disease groups. Especially, for evaluation of apropriateness of the biomarkers, one of the most useful statistical tools is the receiver operating characteristic (ROC) curve. For example, the ROC curve is applied in radiological (Metz, 1986, 1989) and psychiatric medicine (Hsiao et al., 1989). Ordinary the ROC curve is usually based on the normality of distribution of observations for each group. In fact, it is easy to carry out ordinary statistical inference based on the normal distribution. However, observations obtained in real world rarely satisfy this strict assumption. Molodianovitch et al. (2006) have proposed the ROC curve based on the power-normal transformation (Box & Cox, 1964) of the observations, in order to satisfy normality of observations. However, in the approaches which depend on the framework of this "transformation", the ROC curve does not have consistency from estimation of ROC curve to inspection of optimal cutoff value. Then, we provide the power-normal ROC curve assuming the power-normal distribution (Goto et al., 1979, 1983: Goto & Inoue, 1980) as the underling distribution of observations of each group, where the power-normal distribution is defined as the distribution specified before the power-normal transformation.

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