Parametric receiver operating characteristic curve analysis using mathematica

Abstract

Several computer programs have been written to perform receiver operating characteristic (ROC) curve analysis, and are available in the public domain. Here, the author provides the theory and description for ‘rocMath’, a Mathematica program that performs parametric ROC curve analysis. The ‘rocMath’ program has some advantages over other ROC curve programs, including the ability to provide, through optional arguments: (a) user-specified pointwise confidence limits, as well as default 95% limits, on ROC curve area and on true-positive rates; (b) ROC curve plots with data points, a fitted curve, and user-specified pointwise confidence bands; and (c) ROC curve areas, tables, and plots based on a logistic distribution as well as on a standard normal distribution. In addition, the code of ‘rocMath’ can be modified to address additional ROC curve applications. The program uses Mathematica's ability to operate on purely symbolic as well as numeric data to achieve substantial coding efficiency. Limitations of the ‘rocMath’ program are also discussed.