Dynamics of cancer recurrence

Annals of Applied Probability

Volumn 23, Issue 4, 2013, Pages 1437-1468

  Foo, Jasmine ^a   Leder, Kevin ^a  

^a University of Minnesota   (United States)

Author keywords

Branching processes; Cancer; Population genetics

Indexed keywords

EID: 84879741512     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AAP876     Document Type: Article

References (22)

1. BILLINGSLEY, P. (1999). Convergence of Probability Measures, 2nd ed. Wiley, New York. MR1700749
2. CHMIELECKI, J., FOO, J. et al. (2011). Optimization of dosing for EGFR-mutant non-small cell lung cancer with evolutionary cancer modeling. Science Translational Medicine 3 90ra59.
3. COLDMAN, A. J. and GOLDIE, J. H. (1986). A stochastic model for the origin and treatment of tumors containing drug-resistant cells. Bull. Math. Biol. 48 279-292. MR0876300
4. FOO, J. andMICHOR, F. (2010). Evolution of resistance to anti-cancer therapy during general dosing schedules. J. Theoret. Biol. 263 179-188.
5. GOLDIE, J. H. and COLDMAN, A. J. (1979). A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate. Cancer Treat. Rep. 63 1727-1733.
6. GOLDIE, J. H. and COLDMAN, A. J. (1983). Quantitative model for multiple levels of drug resistance in clinical tumors. Cancer Treat. Rep. 67 923-931.
7. HARNEVO, L. andAGUR, Z. (1992). Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency. Cancer Chemotherapy Pharmacology 30 469-476.
8. HARNEVO, L. E. and AGUR, Z. (1991). The dynamics of gene amplification described as a multitype compartmental model and as a branching process. Math. Biosci. 103 115-138. MR1090045
9. IWASA, Y., MICHOR, F. and NOWAK, M. A. (2003). Evolutionary dynamics of escape from biomedical intervention. Proc. Roy. Soc. Lond. B 270 2572-2578.
10. JAGERS, P., KLEBANER, F. C. and SAGITOV, S. (2007). Markovian paths to extinction. Adv. in Appl. Probab. 39 569-587. MR2343678
11. JAGERS, P., KLEBANER, F. C. and SAGITOV, S. (2007). On the path to extinction. Proc. Natl. Acad. Sci. USA 104 6107-6111. MR2578766
12. KOMAROVA, N. (2006). Stochastic modeling of drug resistance in cancer. J. Theoret. Biol. 239 351-366. MR2223739
13. KOMAROVA, N. L. andWODARZ, D. (2005). Drug resistance in cancer: Principles of emergence and prevention. Proc. Natl. Acad. Sci. USA 102 9714-9719.
14. MICHAELSON, J. S., HALPERN, E. and KOPANS, D. B. (1999). Breast cancer: Computer simulation method for estimating optimal intervals for screening. Radiology 212 551-560.
15. MICHOR, F.,NOWAK, M. A. and IWASA, Y. (2006). Evolution of resistance to cancer therapy. Curr. Pharm. Design 12 261-271.
16. OLLER, A. R., RASTOGI, P., MORGENTHALER, S. and THILLY, W. G. (1989). A statistical model to estimate variance in long term-low dose mutation assays: Testing of the model in a human lymphoblastoid mutation assay. Mutat. Res. 216 149-161.
17. PAKES, A. G. (1989). Asymptotic results for the extinction time of Markov branching processes allowing emigration. I. Random walk decrements. Adv. in Appl. Probab. 21 243-269. MR0997723
18. PAO, W. and CHMIELECKI, J. (2010). Rational, biologically based treatment of EGFR-mutant non-small-cell lung cancer. Nat. Rev. Cancer 10 760-774.
19. SAGITOV, S. and SERRA, M. C. (2009). Multitype Bienaymé-Galton- Watson processes escaping extinction. Adv. in Appl. Probab. 41 225-246. MR2514952
20. SEHL, M., ZHOU, H., SINSHEIMER, J. S. and LANGE, K. L. (2011). Extinction models for cancer stem cell therapy. Math. Biosci. 234 132-146. MR2907020
21. SESHADRI, R.,KUTLACA, R. J., TRAINOR, K.,MATTHEWS, C. and MORLEY, A. A. (1987). Mutation rate of normal and malignant human lymphocytes. Cancer Res. 263 407-409.
22. WU, X. andKIMMEL, M. (2010). A note on the path to extinction of critical Markov branching processes. Statist. Probab. Lett. 80 263-269. MR2593561