Statistics and Its Interface

Volume 5 (2012)

Number 3

Imputation-based empirical likelihood inference for the area under the ROC curve with missing data

Pages: 319 – 329

DOI: http://dx.doi.org/10.4310/SII.2012.v5.n3.a4

Authors

Gengsheng Qin (Department of Mathematics and Statistics, Georgia State University, Atlanta, Ga., U.S.A.)

Binhuan Wang (Department of Mathematics and Statistics, Georgia State University, Atlanta, Ga., U.S.A.)

Abstract

In a continuous diagnostic test, the area under the receiver operating characteristic curve (AUC) is commonly used to summarize the diagnostic accuracy of the test. Many current studies on inference of the AUC focus on the complete data case. In this paper, an imputation-based profile empirical likelihood ratio is defined and shown to asymptotically follow a scaled chi-square distribution. Then an empirical likelihood confidence interval for the AUC with missing data is proposed by using the scaled chi-square distribution. The proposed empirical likelihood inference for the AUC is also extended to stratified random samples, and the limiting distribution of the empirical log-likelihood ratio is a weighted summation of independent chi-square distributions with one degree of freedom. Simulation studies are conducted to evaluate the finite sample performance of the proposed method in terms of coverage probability. Additionally, a real example is used to illustrate the proposed method.

Keywords

AUC, diagnostic test, empirical likelihood, imputation, missing data, ROC

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