An Information-theoretical Model for Breast Cancer Detection

Summary

Objectives: Formal diagnostic modeling is an important line of modern biological and medical research. The construction of a formal diagnostic model consists of two stages: first, the estimation of correlation between model parameters and the disease under consideration; and second, the construction of a diagnostic decision rule using these correlation estimates. A serious drawback of current diagnostic models is the absence of a unified mathematical methodological approach to implementing these two stages. The absence of aunified approach makesthe theoretical/biomedical substantiation of diagnostic rules difficult and reduces the efficacyofactual diagnostic model application. Methods: The present study constructs a formal model for breast cancer detection. The diagnostic model is based on information theory. Normalized mutual information is chosen as the measure of relevance between parameters and the patterns studied. The “nearest neighbor” rule is utilized for diagnosis, while the distance between elements is the weighted Hamming distance. The model concomitantly employs cellular fluorescence polarization as the quantitative input parameter and cell receptor expression as qualitative parameters.

Results: Twenty-four healthy individuals and 34 patients (not including the subjects analyzed for the model construction) were tested by the model. Twenty-three healthy subjects and 34 patients were correctly diagnosed.

Conclusions: The proposed diagnostic model is an open one,i.e.it can accommodate new additional parameters, which may increase its effectiveness.

Keywords

Formal diagnostic model - normalized mutual information - weighted Hamming distance - breast cancer(BC) - fluorescence polarization (FP)

• References

• 1 Gelfand IM, Rosenfeld BI, Shifrin MA. Essays on Collaboration of Mathematicians and Physicians. Moscow: Nauka; 1989. (Russian)
• 2 Lukas PJF, Abu-Hanna A. Prognostic methods in medicine. Artif Intell Med 1999; 15: 105-119.
• 3 Verhayen CJDM, Duin RPW, Groen FCA, Joosen JC, Verbeek PW. Progress report on pattern recognition. Rep Prog Phys 1980; 43: 785-831.
• 4 Wolberg WH, Mangasarian OL. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proc Natl Acad Sci USA 1990; 87: 9193-9196.
• 5 Mangasarian OL, Street WN, Wolberg WH. Breast cancer diagnosis and prognosis via linear programming. Oper Res 1995; 43: 570-577.
• 6 Blokh D, Afrimzon E, Stambler I, Korech E, Shafran Y, Zurgil N, Deutsch M. Breast cancer detection by Michaelis-Menten constants via linear programming. Comp Meth Prog Biomed 2007; 85: 210-213.
• 7 Floyd CE, Yun AJ, Sullivan D, Kornguth P. Prediction of breast cancer malignancy using an artificial neural network. Cancer 1994; 74: 2944-2998.
• 8 Furundzic D, Djordjevic M, Bekic AJ. Neural networks approach to early breast cancer detection. J Syst Architect 1998; 44: 617-633.
• 9 Setiono R. Generating concise and accurate classification rules for breast cancer diagnosis. Artif Intell Med 2000; 18: 205-219.
• 10 Shannon CE. A mathematical theory of communication. Bell Syst Tech J 1948; 27: 379-423 623-656.
• 11 Khinchin AI. Mathematical Foundations of Information Theory. New York: Dover; 1957
• 12 Hamming RW. Coding and Information Theory. Englewood Cliffs NJ: Prentice Hall; 1986
• 13 Cover TM, Thomas JA. Elements of Information Theory. New York: Wiley; 1991
• 14 Wolberg WH. Inhibition of migration of human autogenous and allogeneic leukocytes by extracts of patients’ cancers. Cancer Res 1971; 31: 798-802.
• 15 Shapiro HM. Practical Flow Cytometry (3rd ed.). New York: Alan R Liss Inc; 1995
• 16 Kaplan M, Trebnyikov E, Berke G. Fluorescence depolarization as an early measure of T Lymphocyte stimulation. J Immunol Methods 1997; 201: 15-24.
• 17 Hayes DF. Tumor markers for breast cancer. Ann Oncol 1993; 4: 807-819.
• 18 Disis ML, Knutson KL, Schiffman K, Rinn K, McNeel DG. Pre-existent immunity to the HER-2/neo oncogenic protein in patients with HER-2/neu overexpressing breast and ovarian cancer. Breast Cancer Res Treat 2000; 62: 245-252.
• 19 Nicolis G, Prigogine I. Exploring Complexity. New York: WH Freeman and Company; 1990
• 20 Chou WC, Neifeld MA, Xuan R. Informationbased optical design for binary-valued imagery. Appl Optics 2000; 39: 1731-1742.
• 21 Tourassi GD, Frederick ED, Floyd Jr. CE. Application of the mutual information criterion for feature selection in computer-aided diagnostics. Med Phys 2001; 28: 2394-2402.
• 22 Zvarova J, Studeny M. Information theoretical approach to constitution and reduction of medical data. Int J Med Inf 1997; 45: 65-74.
• 23 Rényi A. On measures of dependence. Acta Math Acad Sci Hung 1959; 10: 441-451.
• 24 Benish WA. Mutual information as an index of diagnostic test performance. Methods Inf Med 2003; 42: 260-264.
• 25 Fagen RM. Information measures: statistical confidence limits and inference. J Theor Biol 1978; 73: 61-79.
• 26 Blokh ASh.. Graph Schemes and Algorithms. Minsk: Vishaya Shkola; 1987. (Russian).
• 27 D’hulst R, Rodgers GJ. The Hamming distance in the minority game. PhysicaA 1999; 270: 514-525.
• 28 Bell CB. Mutual information and maximal correlation as measures of dependence. Ann Math Stat 1962; 33: 587-595.
• 29 Deutsch M, Tirosh R, Kaufman M, Zurgil N, Weinreb A. Fluorescence polarization as a functional parameter in monitoring living cells: theory and practice. J Fluoresc 2002; 12: 25-44.
• 30 Perrin F. La fluorscence des solutions. Ann Phys (Paris) 1929; 12: 169-275.
• 31 Scutt D, Lancaster GA, Manning JT. Breast asymmetry and predisposition to breast cancer. Breast Can Res 2006; 8: R14.
• 32 Wong STC, Liu KY, Zhou X. Cancer classification and prediction using logistic regression with Bayesian gene selection. J Biomed Inf 2004; 37: 249-259.
• 33 Schwarzer G, Nagata T, Mattern D, Schmelzeisen R, Schumacher M. Comparison of fuzzy inference, logistic regression, and classification trees (CART). Prediction of cervical lymph node metastasis in carcinoma of the tongue. Methods Inf Med 2003; 42: 572-577.
• 34 Buhl A, Zofel P. SPSS Version 10. Addison-Wesley 2001