Nonparametric and semiparametric estimation of the receiver operating characteristic curve

• 成果类型: Article
• 署名作者: Hsieh, FS; Turnbull, BW
• 署名单位: Cornell University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 25-40
• 关键词: roc curve; models; AREA

摘要

The receiver operating characteristic (ROC) curve describes the performance of a diagnostic test used to discriminate between healthy and diseased individuals based on a variable measured on a continuous scale. The data consist of a training set of m responses X(1),...,X(m) from healthy individuals and n responses Y-1,...,Y-n from diseased individuals. The responses are assumed i.i.d. from unknown distributions F and G, respectively. We consider estimation of the ROC curve de fined by 1-G(F-1(1-t)) for 0 less than or equal to t less than or equal to 1 or, equivalently, the ordinal dominance curve (ODC) given by F(G(-1)(t)). First we consider nonparametric estimators based on empirical distribution functions and derive asymptotic properties. Next we consider the so-called semiparametric ''binormal'' model, in which it is assumed that the distributions F and G are normal after some unknown monotonic transformation of the measurement scale. For this model, we propose a generalized least squares procedure and compare it with the estimation algorithm of Dorfman and Alf, which is based on grouped data. Asymptotic results are obtained; small sample properties are examined via a simulation study. Finally, we describe a minimum distance estimator for the ROC curve, which does not require grouping the data.