Estimation of the area under the ROC curve

Abstract

The area under the receiver operating characteristic curve is frequently used as a measure for the effectiveness of diagnostic markers. In this paper we discuss and compare estimation procedures for this area. These are based on (i) the Mann-Whitney statistic; (ii) kernel smoothing; (iii) normal assumptions; (iv) empirical transformations to normality. These are compared in terms of bias and root mean square error in a large variety of situations by means of an extensive simulation study. Overall we find that transforming to normality usually is to be preferred except for bimodal cases where kernel methods can be effective.

ROC analysis for markers with mass at zero

“…Both the bias and RMSE of the two estimators are essentially equivalent. This contrasts with the results of Faraggi and Reiser [6], which for data without spikes at zero found the TN estimators to be generally better in terms of RMSE.…”

“…This paper discusses ROC analysis for marker data that has a mass at zero and (6). Estimation for models (5) and (6) follows using standard methodology resulting in…”

“…where For estimation of (3) Since as exemplified by the CCS marker the "continuous" part of the marker distribution are generally skewed we follow Faraggi and Reiser [6] in recommending that the Box-Cox transformation be first applied to the data on X and Y. More specifically define…”

“…The non-parametric approach for estimating the AUC based on the Mann-Whitney statistic (MW) is the most frequently used. For continuous markers Faraggi and Reiser [6] compared a number of procedures for estimating the AUC and concluded that in many situations a transformed normal approach (TN) performed better than MW. The TN approach is based on applying a Box-Cox power transformation to the data and then applying parametric estimation based on normal theory.…”

“…The TN approach is based on applying a Box-Cox power transformation to the data and then applying parametric estimation based on normal theory. This approach has been found useful when dealing with ROC curves [3,[6][7][8][9][10].…”