메뉴 건너뛰기




Volumn , Issue , 2008, Pages 25-44

Stochastic multistage cancer models: A fresh look at an old approach

Author keywords

Birth and death process; Differential equation; Gamma frailty model; Hazard rate; Initial value problem

Indexed keywords


EID: 84894528870     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812779489_0002     Document Type: Chapter
Times cited : (2)

References (26)
  • 1
    • 0023738069 scopus 로고
    • Heterogeneity in survival analysis
    • Aalen OO. Heterogeneity in survival analysis. Stat. Med. 1988; 7: 1121-1137.
    • (1988) Stat. Med. , vol.7 , pp. 1121-1137
    • Aalen, O.O.1
  • 2
    • 0028713238 scopus 로고
    • Effects of frailty in survival analysis
    • Aalen OO. Effects of frailty in survival analysis. Stat. Methods Med. Res. 1994; 3: 227-243.
    • (1994) Stat. Methods Med. Res. , vol.3 , pp. 227-243
    • Aalen, O.O.1
  • 3
    • 84965187257 scopus 로고
    • The age distribution of cancer and a multi-stage theory of carcinogenesis
    • Armitage P and Doll R. The age distribution of cancer and a multi-stage theory of carcinogenesis. Br. J. Cancer 1954; 8: 1-12.
    • (1954) Br. J. Cancer , vol.8 , pp. 1-12
    • Armitage, P.1    Doll, R.2
  • 6
    • 0026615207 scopus 로고
    • Slowing of mortality at older ages in large medfly cohorts
    • Carey TR, Liedo P, Orozco D and Vaupel JW. Slowing of mortality at older ages in large medfly cohorts. Science 1992; 258: 457-461.
    • (1992) Science , vol.258 , pp. 457-461
    • Carey, T.R.1    Liedo, P.2    Orozco, D.3    Vaupel, J.W.4
  • 9
    • 2542643176 scopus 로고    scopus 로고
    • Genetic variation in cancer predisposition: Mutational decay of a robust genetic control network
    • Frank SA. Genetic variation in cancer predisposition: mutational decay of a robust genetic control network. Proc. Natl. Acad. Sci. USA 2004; 101: 8061-8065.
    • (2004) Proc. Natl. Acad. Sci. USA , vol.101 , pp. 8061-8065
    • Frank, S.A.1
  • 10
    • 0033984511 scopus 로고    scopus 로고
    • Population risk and physiological rate parameters for colon cancer. The union of an explicit model for carcinogenesis with the public health records of the United States
    • Herrero-Jimenez P, Tomita-Mitchell A, Furth EE, Morgenthaler S and Thilly WG. Population risk and physiological rate parameters for colon cancer. The union of an explicit model for carcinogenesis with the public health records of the United States, Mutat. Res. 2000; 447: 73-116.
    • (2000) Mutat. Res. , vol.447 , pp. 73-116
    • Herrero-Jimenez, P.1    Tomita-Mitchell, A.2    Furth, E.E.3    Morgenthaler, S.4    Thilly, W.G.5
  • 12
    • 1942519347 scopus 로고    scopus 로고
    • Aspects of the Armitage-Doll gamma frailty model for cancer incidence data
    • Izumi S and Ohtaki M. Aspects of the Armitage-Doll gamma frailty model for cancer incidence data. Environmetrics 2004; 15: 209-218.
    • (2004) Environmetrics , vol.15 , pp. 209-218
    • Izumi, S.1    Ohtaki, M.2
  • 14
    • 0002821455 scopus 로고
    • Birth-and-death process, and the theory of carcinogenesis
    • Kendall DG. Birth-and-death process, and the theory of carcinogenesis. Biometrika 1960; 47: 13-21.
    • (1960) Biometrika , vol.47 , pp. 13-21
    • Kendall, D.G.1
  • 15
    • 0003291373 scopus 로고    scopus 로고
    • Mutation-selection networks of cancer initiation: Tumor suppressor genes and chromosomal instability
    • Komarova NL, Sengupta A and Nowak MA. Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability. J. Theor. Biol. 2003; 223: 433-450.
    • (2003) J. Theor. Biol. , vol.223 , pp. 433-450
    • Komarova, N.L.1    Sengupta, A.2    Nowak, M.A.3
  • 16
    • 0029564549 scopus 로고
    • 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
    • Little MP. 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 1995; 51: 1278-1291.
    • (1995) Biometrics , vol.51 , pp. 1278-1291
    • Little, M.P.1
  • 17
    • 0018537343 scopus 로고
    • Two-event models for carcinogenesis: Incidence curves for childhood and adult tumors
    • Moolgavkar SH and Venzon DJ. Two-event models for carcinogenesis: incidence curves for childhood and adult tumors. Math. Biosci. 1979; 47: 55-77.
    • (1979) Math. Biosci. , vol.47 , pp. 55-77
    • Moolgavkar, S.H.1    Venzon, D.J.2
  • 18
    • 0013540157 scopus 로고
    • A two-step mutation theory of carcinogenesis
    • Neyman, J. A two-step mutation theory of carcinogenesis. Bull. Int. Stat. Inst. 1961; 38: 123-135.
    • (1961) Bull. Int. Stat. Inst. , vol.38 , pp. 123-135
    • Neyman, J.1
  • 20
    • 0024446737 scopus 로고
    • Calculating the hazard function and probability of tumor for cancer risk assessment when the parameters are time-dependent
    • Quinn DW. Calculating the hazard function and probability of tumor for cancer risk assessment when the parameters are time-dependent. Risk Anal. 1989; 9: 407-413.
    • (1989) Risk Anal. , vol.9 , pp. 407-413
    • Quinn, D.W.1
  • 21
    • 0002731536 scopus 로고
    • Two-stage stochastic model for carcinogenesis with time-dependent parameters
    • Serio G. Two-stage stochastic model for carcinogenesis with time-dependent parameters. Stat. Probab. Lett. 1984; 2: 95-103.
    • (1984) Stat. Probab. Lett. , vol.2 , pp. 95-103
    • Serio, G.1
  • 23
    • 0002309294 scopus 로고
    • Quantitative theories of carcinogenesis
    • Whittemore A and Keller JB. Quantitative theories of carcinogenesis. SIAM Review 1978; 20: 1-30.
    • (1978) SIAM Review , vol.20 , pp. 1-30
    • Whittemore, A.1    Keller, J.B.2
  • 24
    • 0028850386 scopus 로고
    • On the MVK stochastic carcinogenesis model with Erlang distributed cell life lengths
    • Zheng Q. On the MVK stochastic carcinogenesis model with Erlang distributed cell life lengths. Risk Anal. 1995; 15: 495-502.
    • (1995) Risk Anal. , vol.15 , pp. 495-502
    • Zheng, Q.1
  • 25
    • 0031258720 scopus 로고    scopus 로고
    • A unified approach to a class of stochastic carcinogenesis models
    • Zheng Q. A unified approach to a class of stochastic carcinogenesis models. Risk Anal. 1997; 17: 617-624.
    • (1997) Risk Anal. , vol.17 , pp. 617-624
    • Zheng, Q.1
  • 26
    • 0031898366 scopus 로고    scopus 로고
    • To use or not to use? Backward equations in stochastic carcinogenesis models
    • Zheng Q. To use or not to use? Backward equations in stochastic carcinogenesis models. Biometrics 1998; 54: 384-388.
    • (1998) Biometrics , vol.54 , pp. 384-388
    • Zheng, Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.