Using Delong, Fligner, and Birnbaum's Method to Estimate Standard Errors of AUC Regression with Covariates

• Activity Number: 145
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Amy Buros*+ and Jack Tubbs
• Companies: Baylor University and Baylor University
• Keywords: AUC Regression ; Mann-Whitney Statistic ; Standard Errors ; DeLong's Method ; Fligner ; Covariates

Abstract

To investigate distribution free methods for testing covariate adjusted treatment effects, Dodd and Pepe (2003) proposed a semi-parametric logistic regression model for the area under the receiver operating characteristics curve (AUC). The model comes from the observation that the Mann-Whitney statistic is a non-parametric estimate of the AUC. Their result allows one to test hypotheses using distribution free methods when covariates are discrete; however the standard errors from standard software packages are not correct since the Bernoulli data used in the Mann-Whitney statistic are correlated. We present a modification of the analytical DeLong's method, a modification of Fligner's method, and Birnbaum's upper bound as methods for estimating the standard errors when covariates in the logistic regression model are present. We compare these three methods to the bootstrap method suggested by Dodd and Pepe (2003) with a simulation study.