STOCHASTIC AND STATE SPACE MODELS OF CARCINOGENESIS: SOME NEW MODELING APPROACHES - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 84

smoking. Our analysis has shown that a 4-stage homogeneous stochastic
model ts the data well. This model appears to be consistent with the
molecular biological model of squamous cell lung carcinoma proposed by
Wistuba 67 . By assuming a 4-stage model for the data we have obtained the
following results:
(1) The tobacco nicotine is both an initiator and promoter.
(2) The mutation rates can best be described by the Cox regression
model so that j (i; t) = j0 (t) expf j1 (t)x i g; j = 0; 1; similarly, the birth
rates b j (i; t) and the death rates d j (i; t) can best be described by linear
regression models.
(3) The estimates of the mutation rates and proliferation rates appear
to be consistent with biological observations.
8. Acknowledgments
The research of this paper is supported by a research grant from NCI/NIH,
grant number R15113347-01.
References
1. M. Al-Hajj and M.F. Clarke, Self-renewal and solid tumor stem cells, Onco-
gene 23 (2004), 7274-7288.
2. S.B. Baylin, DNA methylation and gene silencing in cancer, Nature Clinical
Practice Oncology, 2 (2005), S4-S11.
3. S.A. Belinsky, Gene-promoter hypermethylation as a biomarker in lung can-
cer, Nature Rev. Cancer, 4 (2004), 707-717.
4. D.R. Bell and G.V. Zant, Stem cells, aging, and cancer:Inevitabilities and
outcomes, Oncogene, 23 (2004), 7290-7296.
5. M.A. Blasco, Telemeres and human diseases: Aging, cancer and beyond, Na-
ture Rev. Genetics, 6 (2005), 611-622.
6. G.E.P. Box and G.C. Tiao, Bayesian Inferences in Statistical Analysis,
Addison-Wesley, Reading, MA, 1973.
7. J. Breivik and G. Gaudernack, Genomic instability, DNA methylation, and
natural selection in colorectal carcinogenesis, Semi. Cancer Biol., 9 (1999),
245-254.
8. D.P. Cahill, K.W. Kinzler, B. Vogelstein, and C. Lengauer, Genetic instability
and Darwinian selection in tumors, Trends Cell Biol., 9 (1999), M57-60.
9. W.E. Cavenee, et al., Genetic origin of mutations predisposing to retinoblas-
toma, Science, 228 (1985), 501-503.
10. A. de la Chapelle, Genetic predisposition to colorectal cancer, Nature Review
Cancer, 4 (2004), 769-780.
11. K.C. Chu, Multi-event model for carcinogenesis: A model for cancer causa-
tion and prevention. In: Carcinogenesis: A Comprehensive Survey Volume