Parametric receiver operating characteristic curve analysis using mathematica

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.

[1]  D. Dorfman,et al.  Maximum likelihood estimation of parameters of signal detection theory—A direct solution , 1968, Psychometrika.

[2]  Calyampudi R. Rao,et al.  Advanced Statistical Methods in Biometric Research. , 1953 .

[3]  R. Centor.  Signal Detectability , 1991, Medical decision making : an international journal of the Society for Medical Decision Making.

[4]  J. C. Ogilvie,et al.  Maximum-likelihood estimation of receiver operating characteristic curve parameters , 1968 .

[5]  W. Hall,et al.  Confidence Bands for Receiver Operating Characteristic Curves , 1993, Medical decision making : an international journal of the Society for Medical Decision Making.

[6]  R. Centor,et al.  Screening for alcohol abuse using CAGE scores and likelihood ratios. , 1991, Annals of internal medicine.

[7]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .

[8]  D. Dorfman,et al.  Maximum-likelihood estimation of parameters of signal-detection theory and determination of confidence intervals—Rating-method data , 1969 .

[9]  L B Lusted,et al.  Signal detectability and medical decision-making. , 1971, Science.

[10]  J. Hanley,et al.  The meaning and use of the area under a receiver operating characteristic (ROC) curve. , 1982, Radiology.

[11]  Stephen Wolfram,et al.  Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[12]  Calyampudi R. Rao,et al.  Advanced Statistical Methods in Biometric Research. , 1953 .

[13]  Centor Rm,et al.  Receiver Operating Characteristics (ROC) Curve Area Analysis Using the ROC ANALYZER. , 1989 .

[14]  Elisa T. Lee,et al.  Use of relative operating characteristic analysis in epidemiology. A method for dealing with subjective judgement. , 1981, American journal of epidemiology.

[15]  W. England,et al.  An Exponential Model Used for optimal Threshold selection on ROC Curues , 1988, Medical decision making : an international journal of the Society for Medical Decision Making.

[16]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[17]  D. Mossman.  Three-way ROCs , 1999, Medical decision making : an international journal of the Society for Medical Decision Making.