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Smooth semiparametric receiver operating characteristic curves for continuous diagnostic tests
Author(s) -
Wan Shuwen,
Zhang Biao
Publication year - 2007
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2726
Subject(s) - estimator , mathematics , receiver operating characteristic , delta method , semiparametric model , statistics , parametric statistics , asymptotic distribution , mean squared error , kernel density estimation , kernel smoother , kernel (algebra) , minimum variance unbiased estimator , semiparametric regression , normal distribution , kernel method , computer science , artificial intelligence , combinatorics , radial basis function kernel , support vector machine
We propose a semiparametric kernel distribution function estimator, based on which a new smooth semiparametric estimator of the receiver operating characteristic (ROC) curve is constructed. We derive the asymptotic bias and variance of the newly proposed distribution function estimator and show that it is more efficient than the traditional non‐parametric kernel distribution estimator. We also derive the asymptotic bias and variance of our new ROC curve estimator and show that it is more efficient than the smooth non‐parametric ROC curve estimator proposed by Zou et al. ( Stat. Med. 1997; 16 :2143–2156) and Lloyd ( J. Am. Stat. Assoc. 1998; 93 :1356–1364). For our proposed estimators, we derive data‐based methods for bandwidth selection. In addition, we present some results on the analysis of two real data sets. Finally, a simulation study is presented to show that our estimators are better than the non‐parametric counterparts in terms of bias, standard error, and mean‐square error. Copyright © 2006 John Wiley & Sons, Ltd.