Some Aspects on the Utility of Distance Measures in Comparing Two MROC Curves

Authors

  • Sameera G Department of Statistics, Ramanujam School of Mathematical Sciences, Pondicherry University, Puducherry, India
  • Vishnu Vardhan R Department of Statistics, Ramanujam School of Mathematical Sciences, Pondicherry University, Puducherry, India

DOI:

https://doi.org/10.15415/mjis.2016.51006

Keywords:

Bhattacharya Distance, Mahalanobis Distance, Mean vectors and Dispersion matrices and Multivariate Receiver Operating Characteristic curve

Abstract

Receiver Operating Characteristic (ROC) curve is a widely used and accepted tool to assess the performance of a classifier or procedure. Apart from this, comparing the procedures or ROC curves is also of interest. A multivariate extension of ROC (MROC) curve that considers a linear combination of several markers for classification was proposed by Sameera, Vishnu Vardhan and Sarma [13]. In the present paper, some inferential procedures are given to compare two MROC curves by means of distance measures based on scores of MROC curve and summary measures such as mean vectors and dispersion matrices. Real and Simulated data sets are used to demonstrate the above proposed inferential aspects.

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References

Aiyi Liu, Schisterman, E. F. & Yan Zhu (2005). On linear combinations of biomarkers to improve diagnostic accuracy. Statistics in Medicine, 24, 37–47. http://dx.doi.org/10.1002/sim.1922 [2] Bendi Venkata Ramana, Prof. M. Surendra Prasad Babu & Prof. N. B. Venkateswarlu (2012). ILPD (Indian Liver Patient Dataset) Data Set, https://archive.ics.uci.edu/ml/datasets/ILPD+(Indian+Liver+Patient+ Dataset).

Feng Gao, Chengjie Xiong, Yan Yan &Zhengjun Zhang (2008). Estimating optimum linear combination of multiple correlated diagnostic tests at a fixed specificity with receiver operating characteristic curves. Journal of Data Science, 6, 1–13.

Gourevitch, V. & Galanter, E. (1967). A significance test for one parameter iso sensitivity functions. Psychometrika, 32, 25–33. http://dx.doi.org/10.1007/BF02289402

Greenhouse, S.W. & Nathan Mantel (1950). The evaluation of diagnostic tests. Biometrics 6(4), 399–412. http://dx.doi.org/10.2307/3001784

Hanley, J. A. & McNeil, B. J. (1982). Meaning and use of the area under a receiver operating characteristics (roc) curves. Radiology, 143, 29–36. http://dx.doi.org/10.1148/radiology.143.1.7063747

Hanley, J. A. & McNeil, B. J. (1983). A method of comparing the areas under receiver operating characteristic curves derived from the same cases. Radiology, 148, 839–843. http://dx.doi.org/10.1148/radiology.148.3.6878708

John, Q. Su & Jun, S. Liu (1993). Linear combinations of multiple diagnostic markers. Journal of American Statistical Association, 88(424), 1350–1355. http://dx.doi.org/10.1080/01621459.1993.10476417

Johnson, R.A. & Wichern, D.W. (2007). Applied Multivariate Statistical Analysis. Pearson Prentice Hall, 6/e.

Marascuilo, L. A. (1970). Extension of the significance test for one parameter signal detection hypotheses. Psychometrika, 35, 237–243. http://dx.doi.org/10.1007/BF02291265

McClish D. K. (1987). Comparing the areas under more than two independent roc curves. Medical Decision Making, 7, 149–155. http://dx.doi.org/10.1177/0272989X8700700305

Metz, C. E. & Kronman, H. B. (1980). Statistical significance tests for binormal roc curves. Journal of Mathematical Psychology, 22, 243–243. http://dx.doi.org/10.1016/0022-2496(80)90020-6

Sameera, G. Vishnu Vardhan, R & Sarma, KVS (2015). Binary Classification using Multivariate Receiver Operating Characteristic curve for Continuous Data. Journal of Biopharmaceutical Statistics, http://dx.doi.org/10.108010543406.2015.1052479.

Vishnu Vardhan, R. Sameera, G. Chandrasekharan, P.A. & Thulasi Beere (2015). Inferential Procedures for Comparing the Accuracy and Intrinsic Measures of Multivariate Receiver Operating Characteristic (MROC) Curve. International Journal of Statistics in Medical Research, 4, 87-93. http://dx.doi.org/10.6000/1929-6029.2015.04.01.10

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Published

2016-09-05

How to Cite

Sameera G, and Vishnu Vardhan R. 2016. “Some Aspects on the Utility of Distance Measures in Comparing Two MROC Curves”. Mathematical Journal of Interdisciplinary Sciences 5 (1):61-80. https://doi.org/10.15415/mjis.2016.51006.

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Articles