American Institute of Mathematical Sciences

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February  2004, 4(1): 297-322. doi: 10.3934/dcdsb.2004.4.297

Stochastic modeling of carcinogenesis: State space models and estimation of parameters

W. Y. Tan 1, , L.-J. Zhang 1, and  C.W. Chen 2,

1. 

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States, United States
2. 

United States Environmental Protection Agency (EPA), Washington DC 20460, United States

Received  December 2002 Revised  September 2003 Published  November 2003

In this paper we have developed a state space model for carcinogenesis. By using this state space model we have also developed statistical procedures to estimate the unknown parameters via multi-level Gibbs sampling method. We have applied this model and the methods to the British physician data on lung cancer with smoking. Our results indicate that the tobacco nicotine is an initiator. If $t > 60$ years old, then the tobacco nicotine is also a promoter.
Keywords: state space model (Kalman filter model), stochastic differential equations, observation model, stochastic system model., multi-level Gibbs sampling method, MVK two-stage model, Multi-event model of carcinogenesis.
Mathematics Subject Classification: 91B7.
Citation: W. Y. Tan, L.-J. Zhang, C.W. Chen. Stochastic modeling of carcinogenesis: State space models and estimation of parameters. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 297-322. doi: 10.3934/dcdsb.2004.4.297
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