System identification and parameter estimation in mathematical medicine： examples demonstrated for prostate cancer
System identification and parameter estimation in mathematical medicine： examples demonstrated for prostate cancer
摘要
We review our studies on how to identify the most appropriate models of diseases, and how to determine their parameters in a quantitative manner given a short time series of biomarkers, using intermittent androgen deprivation therapy of prostate cancer as an example. Recently, it has become possible to estimate the specific parameters of individual patients within a reasonable time by employing the information concerning other previous patients as a prior. We discuss the importance of using multiple mathematical methods simultaneously to achieve a solid diagnosis and prognosis in the future practice of personalized medicine.
We review our studies on how to identify the most appropriate models of diseases, and how to determine their parameters in a quantitative manner given a short time series of biomarkers, using intermittent androgen deprivation therapy of prostate cancer as an example. Recently, it has become possible to estimate the specific parameters of individual patients within a reasonable time by employing the information concerning other previous patients as a prior. We discuss the importance of using multiple mathematical methods simultaneously to achieve a solid diagnosis and prognosis in the future practice of personalized medicine.
参考文献23
-
1Ideta, A. M., Tanaka, G., Takeuchi, T. and Aihara, K. (2008) A mathematical model of intermittent androgen suppression for prostate cancer. J. Nonlinear Sci., 18, 593--614. 被引量：1
-
2Shimada, T. and Aihara, K. (2008) A nonlinear model with competition between prostate tumor cells and its application to intermittent androgen suppression therapy of prostate cancer. Math. Biosci., 214, 134-139. 被引量：1
-
3Hirata, Y., Bruchovsky, N. and Aihara, K, (2010) Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer. J. Theor. Biol., 264, 517 -527. 被引量：1
-
4Jain, H. V., Clinton, S. K., Bhinder, A. and Friedman, A. (2011) Mathematical modeling of prostate cancer progression in response to androgen ablation therapy. Proc. Natl. Acad. Sci. USA, 108, 19701 -19706. 被引量：1
-
5Portz, T., Kuang, Y. and Nagy, J. D. (2012) A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy. AIP Adv., 2, 011002. 被引量：1
-
6Akakura, K., Bruchovsky, N., Goldenberg, S. L., Rennie, E S., Buckley, A. R. and Sullivan, L. D. (1993) Effects of intermittent androgen suppression on androgen-dependent tumors. Apoptosis and serum prostate-specific antigen. Cancer, 71, 2782-2790. 被引量：1
-
7Bruchovsky, N., Klotz, L., Crook, J., Malone, S., Ludgate, C., Morris, W. J., Gleave, M. E. and Goldenberg, S. L. (2006) Final results of the Canadian prospective phase I! trial of intermittent androgen suppression for men in biochemical recurrence after radiotherapy for locally advanced prostate cancer: clinical parameters. Cancer, 107, 389-395. 被引量：1
-
8Bruchovsky, N., Klotz, L., Crook, J. and Goldenberg, S. L. (2007) Locally advanced prostate cancer--biochemical results from a prospective phase II study of intermittent androgen suppression for men with evidence of prostate-specific antigen recurrence after radiotherapy. Cancer, 109, 858 -867. 被引量：1
-
9Crook, J. M., O'Callaghan, C. J., Duncan, G., Deamaley, D. R, Higano, C. S., Horwitz, E. M., Frymire, E., Malone, S., Chin, J., Nabid, A., et al. (2012) Intermittent androgen suppression for rising PSA level after radiotherapy. N. Engl. J. Med., 367, 895- 903. 被引量：1
-
10Hussain, M., Tangen, C. M., Berry, D. L., Higano, C. S., Crawford, E. D., Liu, G., Wilding, G., Prescott, S., Kanaga Sundaram, S., Small, E. J., et al. (2013) Intermittent versus continuous androgen deprivation in prostate cancer. N. Engl. J. Med., 368, 1314-1325. 被引量：1
-
1于莉琦.具有垂直传染的SEIR疾病模型的分支方向[J].哈尔滨师范大学自然科学学报,2016,32(2):43-46.
-
2张珍,孟献青.一种含潜伏期的疾病模型的动力学性态[J].山西大同大学学报（自然科学版）,2012,28(3):8-9.
-
3于莉琦,李文学.具有垂直传染的SEIR疾病模型的Hopf分支分析[J].生物数学学报,2015,30(4):753-757. 被引量：1
-
4Kara N Babaian.Active surveillance for prostate cancer： when to recommend delayed intervention[J].Asian Journal of Andrology,2015,17(6):885-887. 被引量：2
-
5ZHAO Jiwei,SHAO Jun.Approximate Conditional Likelihood for Generalized Linear Models with General Missing Data Mechanism[J].Journal of Systems Science & Complexity,2017,30(1):139-153. 被引量：7
-
6曹磊,周文,张道祥.一类受接种疫苗和媒体报道影响的传染病模型[J].南通大学学报（自然科学版）,2014,13(4):77-81. 被引量：7
-
7张道祥,熊书琴.具有双时滞的SIRS疾病模型的局部稳定性和持久性[J].安徽工程大学学报,2014,29(3):87-92.
-
8陶龙,曹磊,周文,张道祥.一类具有时滞的传染病模型的Hopf分支分析[J].杭州师范大学学报（自然科学版）,2016,15(1):81-87. 被引量：3
-
9张道祥,曹磊.一类具有非线性发生率的SEIR疾病模型的稳定性和分支分析[J].高校应用数学学报（A辑）,2015,0(2):157-164.
-
10曾晓云,侯成敏,胡正高.一类带脉冲呼吸系统疾病模型的周期解的存在性[J].延边大学学报（自然科学版）,2015,41(1):5-9.
