Improper Multivariate Receiver Operating Characteristic (iMROC) Curve

  • S Balaswamy Indira Gandhi National Tribal University
  • R V. Vardhan Pondicherry University
  • G Sameera Biostatistics and Pharmacometrics, Global Drug Development, Novartis Healthcare Private Limited
Keywords: MROC Curve, AUC, Improper MROC Curve, Inflection and Crossing Point.


In a multivariate setup, the classification techniques have its significance in identifying the exact status of the individual/observer along with accuracy of the test. One such classification technique is the Multivariate Receiver Operating Characteristic (MROC) Curve. This technique is well known to explain the extent of correct classification with the curve above the random classifier (guessing line) when it satisfies all of its properties especially the property of increasing likelihood ratio function. However, there are circumstances where the curve violates the above property. Such a curve is termed as improper curve. This paper demonstrates the methodology of improperness of the MROC Curve and ways of measuring it. The methodology is explained using real data sets.


Bendi VenkataRamana, M. Surendra Prasad Babu and N. B. Venkateswarlu, ILPD (Indian Liver Patient Dataset) Data Set,, 2012.

Chang, Y. C. I., and Park, E., Constructing the best linear combination of diagnostic markers via sequential sampling, Statistics and Probability Letters, 79(18), 1921-1927, 2009.

Green, D. M., and Swets, J. A., Signal Detection theory and Psychophysics, New York, NY: Wiley, 1966.

Krzanowski, W. J., and Hand, D. J., ROC curves for continuous data, Monographs on Statistics and Applied Probability, New York, NY: CRC Press, Taylor and Francis Group, 2009.

Liu A, Schisterman E F, and Zhu Y., On linear combinations of biomarkers to improve diagnostic accuracy, Stat. Med, 24:37-47, 2005.

Lusted, L. B., Signal detectability and medical decision making, Science, 171, 1217-1219, 1971.

Pepe, M., The statistical evaluation of medical tests for classification and prediction, Oxford; New York, 2003.

Reiser B and Farragi D, Confidence Intervals for the generalized ROC criterian, Biometrics, 53: 644-652, 1997.

Sameera G, Vishnu Vardhan R, and Sarma KVS., Binary classification using multivariate receiver operating characteristic curve for continuous data, J Biopharm Stat, 26 (3): 421-431, 2016.

Schisterman Enrique, Faraggi David and Reiser Benjamin., Adjusting the Generalized ROC Curve for Covariates, Statistics in medicine. 23. 3319-31. 10.1002/sim.1908, 2004.

Su JQ and Liu JS., Linear combinations of multiple diagnostic markers, J. Am. Stat. Assoc, 88(424):1350-1355, 1993.

Tanner, J. W. P., and Swets, J. A., A decision-making theory of visual detection, Psychological Review, 61, 401-409, 1954.

Zheng Yuan and Debashis Ghosh, Combining Multiple Biomarker Models in Logistic Regression, Biometrics, 64: 431-439, 2008.

How to Cite
Balaswamy, S., V. Vardhan, R., & Sameera, G. (2020). Improper Multivariate Receiver Operating Characteristic (iMROC) Curve. Statistics, Optimization & Information Computing, 9(2), 492-501.
Research Articles