Smoothed Empirical Likelihood Inference for ROC Curves with Missing Data

Yueheng An

doi:10.4236/ojs.2012.21003

Abstract

The receiver operating characteristic (ROC) curve has been widely used in scientific research fields. After using the random hot deck imputation, we propose the smoothed empirical likelihood ratio statistic for the ROC curve with missing data. Its asymptotic distribution is a scaled chi-square distribution and empirical likelihood confidence intervals for ROC curves are constructed. The simulation study shows that the proposed interval estimates perform well based on the coverage probability for different sample sizes and response rates.

Highlights

The receiver operating characteristic (ROC) curve has been extensively used to evaluate the diagnostic tests
After using the random hot deck imputation, we propose the smoothed empirical likelihood ratio statistic for the ROC curve with missing data
For each fixed response rate and sample size, the coverage probability of confidence intervals for the ROC curve is close to the nominal level

Summary

Introduction

The receiver operating characteristic (ROC) curve has been extensively used to evaluate the diagnostic tests. Qin and Qian [10] proposed smoothing EL interval estimation for the difference of two quantiles with missing data. Motivated by their idea, we propose empirical likelihood ratio for the ROC curve with missing data and prove that the resulting EL ratio has a scaled chi-squared limiting distribution.

Main Results

Simulation Studies

Discussion