Incorporating observability thresholds of tumors into the two-stage carcinogenesis model

Mathematical Biosciences

Volumn 163, Issue 1, 2000, Pages 75-89

  Smith, Marjo V ^a   Portier, Christopher J ^b  

^a Research Triangle Institute   (United States)

^b NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES   (United States)

Author keywords

Backward Kolmogorov equation; Non homogeneous coefficients; Rodent tumor analysis

Indexed keywords

ARTICLE; CARCINOGENESIS; CARCINOGENICITY; MALIGNANT NEOPLASTIC DISEASE; MALIGNANT TRANSFORMATION; OBSERVER VARIATION; POPULATION MODEL; TUMOR GROWTH; TUMOR MODEL;

ANIMALS; LIKELIHOOD FUNCTIONS; LIVER NEOPLASMS; MALE; MODELS, BIOLOGICAL; NEOPLASM RECURRENCE, LOCAL; NEOPLASTIC PROCESSES; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; RATS; RATS, INBRED F344;

EID: 0033978867     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(99)00048-6     Document Type: Article

References (20)

1. Moolgavkar S., Venzon D. Two-event models for carcinogenesis: incidence curves for childhood and adult tumors. Math. Biosci. 47:1979;55.
2. Moolgavkar S., Knudson A.G. Mutation and cancer: a model for human carcinogenesis. J. Nat. Cancer Inst. 66:1981;1037.
3. Kopp-Schneider A., Portier C. Carcinoma formation in MNRI mouse skin painting studies is a process suggesting greater than two stages. Carcinogenesis. 16:1995;53.
4. Luebeck E.G., Moolgavkar S.H. Simulating the process of malignant transformation. Math. Biosci. 123:1994;127.
5. Tsodikov A.D., Asselain B., Yakovlev A.Y. A distribution of tumor size at detection: an application to breast cancer data. Biometrics. 53:1997;1495.
6. Dewanji A., Moolgavkar S.H., Luebeck E.G. Two-mutation model for carcinogenesis: joint analysis of premalignant and malignant lesions. Math. Biosci. 104:1991;97.
7. Moolgavkar S.H., Luebeck E.G. Two-event model for carcinogenesis, mathematical and statistical considerations. Risk Anal. 10:1990;323.
8. Portier C.J., Kopp-Schneider A., Sherman C.D. Calculating tumor incidence rates in stochastic models of carcinogenesis. Math. Biosci. 135:1996;129.
9. Taylor H.M., Karlin S. An Introduction to Stochastic Modeling. 1984;79 Academic Press, Orlando, FL.
10. Feller W. An Introduction to Probability Theory and Its Applications Volume I. 1968;468 Wiley, New York.
11. M.P. Little, Are two mutations sufficient to cause cancer? Some generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon, and Knudson, and of the multistage model of Armitage and Doll, Biometrics 51 (1995) 1278.
12. Hanin L.G., Yakovlev A.Y. A nonidentifiability aspect of the two-stage model of carcinogenesis. Risk Anal. 16:1996;711.
13. Conolly R.B., Kimball J.S. Computer simulation of cell growth governed by stochastic processes. Toxicol. Appl. Pharmacol. 124:1994;284.
14. N.T.J. Bailey, The Elements of Stochastic Processes with Applications to the Natural Sciences, Wiley, New York, 1964, p. 94.
15. Carthew P., Maronpot R.R., Foley J.F., Edwards R.E., Nolan B.M. Method for determining whether the number of heapatocytes in rat liver is increased after treatment with the peroxisome proliferator gemfibrozil. J. Appl. Toxicol. 17:1997;47.
16. Portier C.J. Estimating the tumour onset distribution in animal carcinogenesis experiments. Biometrika. 73:1986;371.
17. Fortran powerstation 4.0 and IMSL Libraries for MS Windows 95, Microsoft.
18. Matlab version 5.3.0, MathWorks, 1999.
19. Saaty T.L. Some stochastic processes with absorbing barriers. J. R. Statist. Soc., Ser. B. 23:1961;319.
20. C.D. Sherman, C.J. Portier, Calculation of the cumulative distribution function of the time to an observable tumor, Bull. Math. Biol. (1999) 00, 1-12.