A compact review of Probability Models for Cancer
Main Article Content
Abstract
The target of this paper is to review the main Probability models that have been proposed to examine different problems in (experimental) carcinogenesis. The models have been grouped, classified and analysed, while their necessity was discussed. We were referred Data Analysis for Brest Cancer, which has been faced under different Mathematical lines of approach, as with fractals, information measures, among them.
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How to Cite
KITSOS, Christos P.; NISIOTIS, Constantinos-Symeon.
A compact review of Probability Models for Cancer.
Medical Research Archives, [S.l.], v. 12, n. 10, oct. 2024.
ISSN 2375-1924.
Available at: <https://esmed.org/MRA/mra/article/view/5819>. Date accessed: 22 dec. 2024.
doi: https://doi.org/10.18103/mra.v12i10.5819.
Section
Review Articles
The Medical Research Archives grants authors the right to publish and reproduce the unrevised contribution in whole or in part at any time and in any form for any scholarly non-commercial purpose with the condition that all publications of the contribution include a full citation to the journal as published by the Medical Research Archives.
References
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2. Tan WY. Stochastic Models of Carcinogenesis. Marcel-Dekker, N.Y.;1991
3. Wosniok W, Kitsos C, Watanabe K. Statistical issues in the Application of Multistage and Biologically Based Models. In: Cogliano V, Luebeck G, Zapponi G. eds. Respectives on Biologically Based Cancer Risk Assessment. NATO-Challenges of Modern Society. 1998; Vol. 23:243-272.
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5. Bernal M, Chalikias MS, Kitsos CP. Analysing data set on Thyroid Cancer. In: 2d International Conference on Cancer Risk Assessment (ICCRA2, e-proceedings). 2007; Santorini, 25-27 May 2007.
6. Hayat MJ, Howlader N, Reichman ME, Edwards BK. Cancer statistics, trends, and multiple primary cancer analyses from the Surveillance, Epidemiology, and End Results (SEER). Program Oncologist. 2007; 12:20-37.
7. Angelopoulou R, Bala M, Lavranos G, Chalikias M, Kitsos C, Baka S, Kittas C. Evaluation of immunohistochemical markers of germ cells’ proliferation. In the developing rat testis: A comparative study. Tissue and Cell. 2008; 40(1):43-50
8. Cogliano VJ, Luebeck EG, Zapponi G. Perspectives on Biologically-Based Cancer Risk Assessment eds. NATO Challenges of Modern Society. Kluwer Academic/Plenum Pub. 1999; Vol 23.
9. Chyczewski L, Niklinski J, Pluygers E. Endrocrine Disruptors and Carcinogenic Risk Assessment. NATO Science Series I. IOS Press. Amsterdam; 2002; Vol 340.
10. Edler L, Kitsos, CP. Recent Advances in Qualitative Methods in Cancer and Human Health Risk Assessment. Editors, Wiley, UK; 2005.
11. Moolgavkar SH, Venzon D. Two-Event Modls for Carcinogenesis: Incidence Cures for Childhood and Adult Tumors. Mathem. Biosciences. 1979; 47:55-77.
12. Moolgavkar SH, Knudson A. Mutation and cancer: A model for human carcinogenesis. Journal of the National Cancer Institute. 1981; 66:1037-1052.
13. Luebeck GE, Moolgavkar SH. Two-Event Model for Carcinogenesis: Biological, Mathematical and Statistical Considerations. Risk Analysis. 1989; 10:323-341.
14. Luebeck GE, Moolgavkar SH. Stochastic Description of Initiation and Promotion in Experimental Carcinogenesis. Ann. Ist. Super.Sanita. 1991; 27(4):575-580.
15. Luebeck GE, Moolgavkar SH. Multistage Carcinogenesis: Population-Based Model for Colon Cancer. Journal of National Institute. 1992; 610-618.
16. Kopp-Schneider A. Carcinogenesis models for risk assessment. Stat. Methods in Medical Research. 1997; 6:317-340.
17. Muller CH, Kitsos CP. Optimal Design Criteria Based on Tolerance Regions. In: Di Bucchianno A, Lauter H, Wynn H, eds. MODA7 – Advances in Model-Oriented Design and Analysis. Physica-Verlag. 2004; 107-115.
18. Kitsos CP. Risk Analysis in Practice and Theory. In: Kitsos CP, Oliveira TA, Pierri F, Restaino MR, eds. Statistical Modelling and Risk Analysis. Springer. 2023; 107-118.
19. Kitsos CP. Optimal Design for Bioassays in Carcinogenesis. In: Edler L, Kitsos CP, eds. Quantitative Methods for Cancer and Human Health Risk Assessment. Wiley, England. 2005; 267-279.
20. National Research Council (NCR). Principles of Toxicological Interactions Associated with Multiple Chemical Exposures. National Academic Press. Washington, DC. 1980.
21. Armitage P, Doll R. The Age Distribution of Cancer and a Multi-Stage Theory of Carcinogenesis. Brit. J. Cancer. 1954; 8:1-12.
22. Armitage P. The Assessment of Low Dose Carcinogenicity. Biometrics. 1982; 28 (sup.):119-129.
23. Armitage P. Multistage Models of Carcinogenesis. Environmental Health Perspectives. 1985; 63:195-201.
24. Doll R. The Age Distribution of Cancer: Implications for Models of Carcinogenesis. JRSS. 1971; A134:133-166.
25. Doll R. An Epidemiological Perspective on the Biology of Cancer. Cancer Res. 1978; 38:3573-3583.
26. Cox DR. Regression Models and Life Tables (with discussion). JRSS. 1972; B, 74:187-220.
27. Cox DR, Snell EJ. Analysis of binary data. Second Edition, Chapman and Hall. 1989.
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29. Stehlik M, Hermann P, Giebel S, Schenk JP. Multifractal Analysis on Cancer Risk. In: Oliveira TA, Kitsos CP, Oliveira A, Grilo L, eds. Recent Studies on Risk Analysis and Statistical Modeling. Springer. 2018; 17-34.
30. Losa GA, Nonnenmacher TF. Fractals in biology and medicine. Springer. 2005.
31. Hermann P, Piza S, Ruderstorfer S, Spreitzer S, Stehlik M. Fractal Case Study for Mammary Cancer: Analysis of Interobserver Variability. In: Kitsos CP, Oliveira TA, Rigas A, Gulati S, eds. Theory and Practice of Risk Assessment. Springer. 2015; 21-36.
32. US EPA. Guidelines for exposure assessment. Federal Register. 1992; 51:33992-34003.
33. US EPA. Guidelines for Carcinogenic Risk Assessment. EPA, Washington, DC. 1999.
34. Wosniok W, Kitsos CP, Watanabe K. Statistical issues in the Application of Multistage and Biologically Based Models. In: Cogliano V, Luebeck G, Zapponi G. Respectives on Biologically Based Cancer Risk Assessment. NATO-Challenges of Modern Society. 1998; Vol. 23:243-272.
35. Iverson S, Arley N. On the mechanism of experimental carcinogenesis. 1950; 27:773-803.
36. Nordling CO. A new theory of the cancer inducing mechanism. British J. of Ca. 1953; 7:78-72.
37. McCullagh P, Nelder JA. Generalized Linear Models. Chapman and Hall, London. 1989.
38. Luebeck EG, Watanabe K, Travis C. Biologically based models of carcinogenesis. In: Cogliano VJ, Luebeck EG, Zapponi GA, eds. Prospectives on Biologically Based Cancer Risk Assessment. Kluwer Academic/Plenum Publishers. New York. 1999; 205-241.
39. Hartley HO, Sielken RL. Estimation of ‘Safe Dose’ in Carcinogenic Experiments. Biometrics. 1977; 33:1-30.
40. Finney DJ. Probit Analysis, 3d ed. Cambridge Un. Press. 1971.
41. Dewanji A, Venzon DJ, Moolgavkar SH. A stochastic two-stage model for cancer risk assessment: II. The number and size of premaligmant clones. Risk Analysis. 1989; 9:179-187.
42. Kitsos CP, Limakopoulou A. Optimal Risk Assessment for Estimating the VSD in Experimental Carcinogenesis. In: A. Hasman et al., eds. Medical Infobank for Europe. IOS Press. 2000; 763 – 766.
43. Kitsos CP. Cancer Bioassays: A Statistical Approach. Lampert. 2012.
44. Michaelis L, Menten ML. Kinetics for Intertase action. Biochemische Zeiturg. 1913; 49:333-369.
45. Endrenyi L, Chan FY. Optimal Design of Experiments for the Estimation of Precise Hyperbolic Kinetic and Binding Parameters. J. Theor. Biol. 1981; 90:241-263.
46. Currie DJ. Estimating Michaelis-Menten Parameters: Bias, Variance and Experimental design. Biometrics. 1982; 38:907-919.
47. Gilberg F, Urfer W, Elder L. Heteroscedastic Nonlinear Regression Models with Random Effects and their Application to Enzyme Kinetic Data. Biometrical Journal. 1999; 41:543-557.
48. Toulias TL., Kitsos CP. Fitting the Michaelis-Menten Model. Journal of Comp. and Appl. Math. 2016; 296:303-319.
49. Bates DM, Watts DG. Nonlinear-Regression Analysis and its Applications. Oliver and Boyd, Edinburgh. 1998.
50. Kitsos CP. Design aspects for the Michaelis – Menten Model. Biometrical Letters. 2001; 38:53-66.
51. Kitsos CP. The Cancer Risk Assessment as an Experimental Design. In: Chyczewski L, Niklinski J, Pluygers E, eds. Endocrine Disrupters and Carcinogenic Risk Assessment. IOS Press. 2002; 37:329-337.
52. Risch A, Dally H, Edler L. Genetic Polymorphisms in Metabolising Enzymes as Lung Cancer Risk Factors. In: Edler L, Kitsos CP, eds. Recent Advances in Quantitative Methods in Cancer and Human Risk Assessment. Wiley, UK. 2005.
53. Kitsos CP. Optimal Designs for Estimating the Percentiles of the Risk in Multistage Models in Carcinogenesis. Biometrical Journal. 1999; 41, No 1:33-43.
54. Hu I. On sequential designs in nonlinear problems. Biometrika. 1998; 85:496-503.
55. Kitsos CP. Optimal Designs for Percentiles at Multistage Models in Carcinogenesis. Biometrical Journal. 1997; 41, No 1:33-43.
56. Kitsos CP. Sequential Approaches for Ca Tolerance Models. Biometrie und Medizinische Informatik Greifswalder Seminarberichte. 2011; Heft 18:87-98.
57. Kitsos CP, Edler L. Cancer Risk assessment mixtures. In: Edler L, Kitsos CP, eds. Quantitative Methods for Cancer and Human Health Risk Assessment. Wiley, England. 2005; 283-298.
58. Hodgson E, Levi EP. A textbook of modern toxicology. Elsevier, New York. 1987.
59. Prentice RL, Kalbfleisch JD. Hazard Rate Models with Covariates. Biometrics. 1979; 25-39.
60. Kitsos CP. The Role of Covariates in Experimental Carcinogenesis. Biometrical Letters. 1998; Vol. 35, No 2:95-106.
61. Begg MD, Legakos S. Loss in efficiency caused by omitting covariates and misspecifying exposure in logistic regression models. JASA. 1993; 88:166-170.
62. Berkson J. Maximum Likelihood and Minimum X2 estimates of the logistic function. JASA. 1955; 50:130-162.
63. Breslow ΝΕ, Day ΝΕ. Statistical Methods on Cancer-Research. IARC. Lyon, France. 1980; No 32.
64. Hosmer DW, Lemeshow S. Applied Logistic Regression. John Wiley. 1989.
65. Rao CR, Toutenburg H. Linear Models, 2nd ed. Springer-Verlag, N. Y. 1999.
66. Kitsos CP. On the Logit Methods for Ca Problems. In: Vonta F, ed. Statistical Methods for Biomedical and Technical Systems. Limassol, Cyprus. 2006; 335-340
67. Collet D. Modelling Binary Data. Chapman and Hall/CRC. 1999.
68. Bliss CI. The calculation of the dosage mortality curve. Annals of Applied Biology. 1935; 22:134.
69. Lemeshow S, Hosmer DW. The use of goodness-of fit statistics in the development of logistic regression models. American Journal of Epidemiology. 1982; 115:92-106.
70. Toulias TL, Kitsos CP. Hazard Rate and Future Lifetime for the Generalized Normal Distribution. In: Oliveira TA, Kitsos CP, Oliveira A, Grilo L, eds. Recent Studies on Risk Analysis and Statistical Modeling. Springer. 2018; 165-180.
71. Bugano DD, Conforti-Froes N, Yamaguchi NH, Baracat EC. Genetic polymorphisms, the metabolism of oestrogens and breast cancer: A review. European Journal Gynaecological Oncology. 2008; 29(4):313-20.
72. Feigelson SH, McKean-Cowdlin R, Henderson EB. Concerning the CYP MspA1 and breast cancer risk: a meta-analysis. Mutagenesis. 2002; 17:445-446.
73. Huang CS, Chern HD, Chang KJ, Cheng CW, Hsu SM, Shen CY. Breast Cancer Risk Associated with Genotype Polymorphism of the Oestrogen-metabolizing CYP17, CYP1A1 and COMT: A Multigenic Study on Cancer Susceptibility. Cancer Research. 1999; 59:4870-4875.
74. Kitsos CP. Estimating the Relative Risk for the Breast Cancer. Biometrical Letters. 2010; Vol 47(2):133-146.
75. Kitsos CP, Toulias TL. Generalized Information Criteria for the Best Logit Model. In: Kitsos CP, Oliveira TA, Rigas A, Gulati S, eds. Theory and Practice of Risk Assessment. Springer. 2015; 3-20.
76. Duffy MJ. CA 15-3 and related mucins as circulating markers in breast cancer. Ann Clin Biochem. 1999; 36:579–86.
77. Prentice RL, Gloeckler LA. Regression analysis of grouped survival data with application to breast cancer data. Biometrics. 1978; 34:56-67.
78. Cheung K, Graves CRL, Robertson JFR. Tumour marker measurements in the diagnosis and monitoring of breast cancer. Cancer Treat Review. 2000; 26:91–102.
79. Amaral-Mendes JJ, Pluygers E. Use of Biochemical and Molecular Biomarkers for Cancer Risk Assessment in Humans. In: Cogliano V, Luebeck G, Zapponi G. Respectives on Biologically Based Cancer Risk Assessment. NATO-Challenges of Modern Society. 1999; Vol. 23:81-152.
80. Vineis P, Schatzkin A, Potter JD. Models of carcinogenesis: an overview. Carcinogenesis. 2010; 31(10):1703–1709.
81. Gatenby AR, Vincent LT. An Evolutionary Model of Carcinogenesis. Cancer Research. 2003; 63:6212– 6220.
82. Travis CC, White RK, Ward RC. Interspecies Extrapolation of Pharmacokinetics. J. Theor. Biol. 1990; 42:285-304.
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2. Tan WY. Stochastic Models of Carcinogenesis. Marcel-Dekker, N.Y.;1991
3. Wosniok W, Kitsos C, Watanabe K. Statistical issues in the Application of Multistage and Biologically Based Models. In: Cogliano V, Luebeck G, Zapponi G. eds. Respectives on Biologically Based Cancer Risk Assessment. NATO-Challenges of Modern Society. 1998; Vol. 23:243-272.
4. Zapponni, G. A. Carcinogenetic Risk Assessment: Some Points of Interest for a Discussion. In: Chyczewski L, Niklinski J, Plugers E. eds. Endocrine Disrupters and Carcinogenic Risk Assessment. IOS press. 2002; 15-27.
5. Bernal M, Chalikias MS, Kitsos CP. Analysing data set on Thyroid Cancer. In: 2d International Conference on Cancer Risk Assessment (ICCRA2, e-proceedings). 2007; Santorini, 25-27 May 2007.
6. Hayat MJ, Howlader N, Reichman ME, Edwards BK. Cancer statistics, trends, and multiple primary cancer analyses from the Surveillance, Epidemiology, and End Results (SEER). Program Oncologist. 2007; 12:20-37.
7. Angelopoulou R, Bala M, Lavranos G, Chalikias M, Kitsos C, Baka S, Kittas C. Evaluation of immunohistochemical markers of germ cells’ proliferation. In the developing rat testis: A comparative study. Tissue and Cell. 2008; 40(1):43-50
8. Cogliano VJ, Luebeck EG, Zapponi G. Perspectives on Biologically-Based Cancer Risk Assessment eds. NATO Challenges of Modern Society. Kluwer Academic/Plenum Pub. 1999; Vol 23.
9. Chyczewski L, Niklinski J, Pluygers E. Endrocrine Disruptors and Carcinogenic Risk Assessment. NATO Science Series I. IOS Press. Amsterdam; 2002; Vol 340.
10. Edler L, Kitsos, CP. Recent Advances in Qualitative Methods in Cancer and Human Health Risk Assessment. Editors, Wiley, UK; 2005.
11. Moolgavkar SH, Venzon D. Two-Event Modls for Carcinogenesis: Incidence Cures for Childhood and Adult Tumors. Mathem. Biosciences. 1979; 47:55-77.
12. Moolgavkar SH, Knudson A. Mutation and cancer: A model for human carcinogenesis. Journal of the National Cancer Institute. 1981; 66:1037-1052.
13. Luebeck GE, Moolgavkar SH. Two-Event Model for Carcinogenesis: Biological, Mathematical and Statistical Considerations. Risk Analysis. 1989; 10:323-341.
14. Luebeck GE, Moolgavkar SH. Stochastic Description of Initiation and Promotion in Experimental Carcinogenesis. Ann. Ist. Super.Sanita. 1991; 27(4):575-580.
15. Luebeck GE, Moolgavkar SH. Multistage Carcinogenesis: Population-Based Model for Colon Cancer. Journal of National Institute. 1992; 610-618.
16. Kopp-Schneider A. Carcinogenesis models for risk assessment. Stat. Methods in Medical Research. 1997; 6:317-340.
17. Muller CH, Kitsos CP. Optimal Design Criteria Based on Tolerance Regions. In: Di Bucchianno A, Lauter H, Wynn H, eds. MODA7 – Advances in Model-Oriented Design and Analysis. Physica-Verlag. 2004; 107-115.
18. Kitsos CP. Risk Analysis in Practice and Theory. In: Kitsos CP, Oliveira TA, Pierri F, Restaino MR, eds. Statistical Modelling and Risk Analysis. Springer. 2023; 107-118.
19. Kitsos CP. Optimal Design for Bioassays in Carcinogenesis. In: Edler L, Kitsos CP, eds. Quantitative Methods for Cancer and Human Health Risk Assessment. Wiley, England. 2005; 267-279.
20. National Research Council (NCR). Principles of Toxicological Interactions Associated with Multiple Chemical Exposures. National Academic Press. Washington, DC. 1980.
21. Armitage P, Doll R. The Age Distribution of Cancer and a Multi-Stage Theory of Carcinogenesis. Brit. J. Cancer. 1954; 8:1-12.
22. Armitage P. The Assessment of Low Dose Carcinogenicity. Biometrics. 1982; 28 (sup.):119-129.
23. Armitage P. Multistage Models of Carcinogenesis. Environmental Health Perspectives. 1985; 63:195-201.
24. Doll R. The Age Distribution of Cancer: Implications for Models of Carcinogenesis. JRSS. 1971; A134:133-166.
25. Doll R. An Epidemiological Perspective on the Biology of Cancer. Cancer Res. 1978; 38:3573-3583.
26. Cox DR. Regression Models and Life Tables (with discussion). JRSS. 1972; B, 74:187-220.
27. Cox DR, Snell EJ. Analysis of binary data. Second Edition, Chapman and Hall. 1989.
28. Kitsos CP. Sir David Cox: A wise and noble statistician (1924–2022). Eur. Math. Soc. Mag. 2022; 27 – 32.
29. Stehlik M, Hermann P, Giebel S, Schenk JP. Multifractal Analysis on Cancer Risk. In: Oliveira TA, Kitsos CP, Oliveira A, Grilo L, eds. Recent Studies on Risk Analysis and Statistical Modeling. Springer. 2018; 17-34.
30. Losa GA, Nonnenmacher TF. Fractals in biology and medicine. Springer. 2005.
31. Hermann P, Piza S, Ruderstorfer S, Spreitzer S, Stehlik M. Fractal Case Study for Mammary Cancer: Analysis of Interobserver Variability. In: Kitsos CP, Oliveira TA, Rigas A, Gulati S, eds. Theory and Practice of Risk Assessment. Springer. 2015; 21-36.
32. US EPA. Guidelines for exposure assessment. Federal Register. 1992; 51:33992-34003.
33. US EPA. Guidelines for Carcinogenic Risk Assessment. EPA, Washington, DC. 1999.
34. Wosniok W, Kitsos CP, Watanabe K. Statistical issues in the Application of Multistage and Biologically Based Models. In: Cogliano V, Luebeck G, Zapponi G. Respectives on Biologically Based Cancer Risk Assessment. NATO-Challenges of Modern Society. 1998; Vol. 23:243-272.
35. Iverson S, Arley N. On the mechanism of experimental carcinogenesis. 1950; 27:773-803.
36. Nordling CO. A new theory of the cancer inducing mechanism. British J. of Ca. 1953; 7:78-72.
37. McCullagh P, Nelder JA. Generalized Linear Models. Chapman and Hall, London. 1989.
38. Luebeck EG, Watanabe K, Travis C. Biologically based models of carcinogenesis. In: Cogliano VJ, Luebeck EG, Zapponi GA, eds. Prospectives on Biologically Based Cancer Risk Assessment. Kluwer Academic/Plenum Publishers. New York. 1999; 205-241.
39. Hartley HO, Sielken RL. Estimation of ‘Safe Dose’ in Carcinogenic Experiments. Biometrics. 1977; 33:1-30.
40. Finney DJ. Probit Analysis, 3d ed. Cambridge Un. Press. 1971.
41. Dewanji A, Venzon DJ, Moolgavkar SH. A stochastic two-stage model for cancer risk assessment: II. The number and size of premaligmant clones. Risk Analysis. 1989; 9:179-187.
42. Kitsos CP, Limakopoulou A. Optimal Risk Assessment for Estimating the VSD in Experimental Carcinogenesis. In: A. Hasman et al., eds. Medical Infobank for Europe. IOS Press. 2000; 763 – 766.
43. Kitsos CP. Cancer Bioassays: A Statistical Approach. Lampert. 2012.
44. Michaelis L, Menten ML. Kinetics for Intertase action. Biochemische Zeiturg. 1913; 49:333-369.
45. Endrenyi L, Chan FY. Optimal Design of Experiments for the Estimation of Precise Hyperbolic Kinetic and Binding Parameters. J. Theor. Biol. 1981; 90:241-263.
46. Currie DJ. Estimating Michaelis-Menten Parameters: Bias, Variance and Experimental design. Biometrics. 1982; 38:907-919.
47. Gilberg F, Urfer W, Elder L. Heteroscedastic Nonlinear Regression Models with Random Effects and their Application to Enzyme Kinetic Data. Biometrical Journal. 1999; 41:543-557.
48. Toulias TL., Kitsos CP. Fitting the Michaelis-Menten Model. Journal of Comp. and Appl. Math. 2016; 296:303-319.
49. Bates DM, Watts DG. Nonlinear-Regression Analysis and its Applications. Oliver and Boyd, Edinburgh. 1998.
50. Kitsos CP. Design aspects for the Michaelis – Menten Model. Biometrical Letters. 2001; 38:53-66.
51. Kitsos CP. The Cancer Risk Assessment as an Experimental Design. In: Chyczewski L, Niklinski J, Pluygers E, eds. Endocrine Disrupters and Carcinogenic Risk Assessment. IOS Press. 2002; 37:329-337.
52. Risch A, Dally H, Edler L. Genetic Polymorphisms in Metabolising Enzymes as Lung Cancer Risk Factors. In: Edler L, Kitsos CP, eds. Recent Advances in Quantitative Methods in Cancer and Human Risk Assessment. Wiley, UK. 2005.
53. Kitsos CP. Optimal Designs for Estimating the Percentiles of the Risk in Multistage Models in Carcinogenesis. Biometrical Journal. 1999; 41, No 1:33-43.
54. Hu I. On sequential designs in nonlinear problems. Biometrika. 1998; 85:496-503.
55. Kitsos CP. Optimal Designs for Percentiles at Multistage Models in Carcinogenesis. Biometrical Journal. 1997; 41, No 1:33-43.
56. Kitsos CP. Sequential Approaches for Ca Tolerance Models. Biometrie und Medizinische Informatik Greifswalder Seminarberichte. 2011; Heft 18:87-98.
57. Kitsos CP, Edler L. Cancer Risk assessment mixtures. In: Edler L, Kitsos CP, eds. Quantitative Methods for Cancer and Human Health Risk Assessment. Wiley, England. 2005; 283-298.
58. Hodgson E, Levi EP. A textbook of modern toxicology. Elsevier, New York. 1987.
59. Prentice RL, Kalbfleisch JD. Hazard Rate Models with Covariates. Biometrics. 1979; 25-39.
60. Kitsos CP. The Role of Covariates in Experimental Carcinogenesis. Biometrical Letters. 1998; Vol. 35, No 2:95-106.
61. Begg MD, Legakos S. Loss in efficiency caused by omitting covariates and misspecifying exposure in logistic regression models. JASA. 1993; 88:166-170.
62. Berkson J. Maximum Likelihood and Minimum X2 estimates of the logistic function. JASA. 1955; 50:130-162.
63. Breslow ΝΕ, Day ΝΕ. Statistical Methods on Cancer-Research. IARC. Lyon, France. 1980; No 32.
64. Hosmer DW, Lemeshow S. Applied Logistic Regression. John Wiley. 1989.
65. Rao CR, Toutenburg H. Linear Models, 2nd ed. Springer-Verlag, N. Y. 1999.
66. Kitsos CP. On the Logit Methods for Ca Problems. In: Vonta F, ed. Statistical Methods for Biomedical and Technical Systems. Limassol, Cyprus. 2006; 335-340
67. Collet D. Modelling Binary Data. Chapman and Hall/CRC. 1999.
68. Bliss CI. The calculation of the dosage mortality curve. Annals of Applied Biology. 1935; 22:134.
69. Lemeshow S, Hosmer DW. The use of goodness-of fit statistics in the development of logistic regression models. American Journal of Epidemiology. 1982; 115:92-106.
70. Toulias TL, Kitsos CP. Hazard Rate and Future Lifetime for the Generalized Normal Distribution. In: Oliveira TA, Kitsos CP, Oliveira A, Grilo L, eds. Recent Studies on Risk Analysis and Statistical Modeling. Springer. 2018; 165-180.
71. Bugano DD, Conforti-Froes N, Yamaguchi NH, Baracat EC. Genetic polymorphisms, the metabolism of oestrogens and breast cancer: A review. European Journal Gynaecological Oncology. 2008; 29(4):313-20.
72. Feigelson SH, McKean-Cowdlin R, Henderson EB. Concerning the CYP MspA1 and breast cancer risk: a meta-analysis. Mutagenesis. 2002; 17:445-446.
73. Huang CS, Chern HD, Chang KJ, Cheng CW, Hsu SM, Shen CY. Breast Cancer Risk Associated with Genotype Polymorphism of the Oestrogen-metabolizing CYP17, CYP1A1 and COMT: A Multigenic Study on Cancer Susceptibility. Cancer Research. 1999; 59:4870-4875.
74. Kitsos CP. Estimating the Relative Risk for the Breast Cancer. Biometrical Letters. 2010; Vol 47(2):133-146.
75. Kitsos CP, Toulias TL. Generalized Information Criteria for the Best Logit Model. In: Kitsos CP, Oliveira TA, Rigas A, Gulati S, eds. Theory and Practice of Risk Assessment. Springer. 2015; 3-20.
76. Duffy MJ. CA 15-3 and related mucins as circulating markers in breast cancer. Ann Clin Biochem. 1999; 36:579–86.
77. Prentice RL, Gloeckler LA. Regression analysis of grouped survival data with application to breast cancer data. Biometrics. 1978; 34:56-67.
78. Cheung K, Graves CRL, Robertson JFR. Tumour marker measurements in the diagnosis and monitoring of breast cancer. Cancer Treat Review. 2000; 26:91–102.
79. Amaral-Mendes JJ, Pluygers E. Use of Biochemical and Molecular Biomarkers for Cancer Risk Assessment in Humans. In: Cogliano V, Luebeck G, Zapponi G. Respectives on Biologically Based Cancer Risk Assessment. NATO-Challenges of Modern Society. 1999; Vol. 23:81-152.
80. Vineis P, Schatzkin A, Potter JD. Models of carcinogenesis: an overview. Carcinogenesis. 2010; 31(10):1703–1709.
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