Receiver Operating Characteristic (ROC) Curve-Based Variable Selection for Logistic Regression Models

• Activity Number: 342
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jodi Lapidus*+ and Mara Tableman and Aaron Baraff
• Companies: Oregon Health & Science University and Portland State University and Oregon Health & Science University
• Keywords: logistic regression ; biomarkers ; variable selection ; ROC curves

Abstract

Many recent investigations have been dedicated to identifying and evaluating biomarkers, and these studies often focus on combining information from multiple markers to classify disease. While there are ample classification methods proposed in the literature, Pepe (2003) showed that decision rules based on the likelihood ratio function, or equivalently, the risk score, are optimal. Logistic regression can be used to generate a risk score, and the c-statistic or area under the ROC curve (AUROC) can be computed to assess classification performance. When several candidate biomarkers are collected, it is labor-intensive to check performance of all possible combinations. We outline a procedure to select markers for inclusion in a logistic regression model based on improvement in AUROC. We note the equivalence of a non-parametric two-sample test statistic and AUROC, and use this to select the first marker for the model. We make use of the jagged ordered multivariate optimization algorithm for partial ROC curves outlined in Baker (2000). We illustrate our algorithm on various sized datasets, and contrast the results to models fit with standard variable selection methods.