Significance Analysis of ROC Indices for Comparing Diagnostic Markers: Applications to Gene Microarray Data

Abstract

A common objective in microarray experiments is to select genes that are differentially expressed between two classes (two treatment groups). Selection of differentially expressed genes involves two steps. The first step is to calculate a discriminatory score that will rank the genes in order of evidence of differential expressions. The second step is to determine a cutoff for the ranked scores. Summary indices of the receiver operating characteristic (ROC) curve provide relative measures for a ranking of differential expressions. This article proposes using the hypothesis-testing approach to compute the raw p-values and/or adjusted p-values for three ROC discrimination measures. A cutoff p-value can be determined from the (ranked) p-values or the adjusted p-values to select differentially expressed genes. To quantify the degree of confidence in the selected top-ranked genes, the conditional false discovery rate (FDR) over the selected gene set and the “Type I” (false positive) error probability for each selected gene are estimated. The proposed approach is applied to a public colon tumor data set for illustration. The selected gene sets from three ROC summary indices and the commonly used two-sample t-statistic are applied to the sample classification to evaluate the predictability of the four discrimination measures.

Key Words:

• Colon tumor dataset
• Familywise error rate (FWE)
• False discovery rate (FDR)
• Number of true null hypotheses
• Receiver operating characteristic curve

Mathematics Subject Classification:

• 62P10
• 92B15

Acknowledgments