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題名 慢性B型肝炎病毒感染之年齡相關模型及存活機率分析
An age-dependent model with survival analysis on chronic hepatitis b virus infection作者 陳炘毓
Chen, Shin Yu貢獻者 陸行
Luh, Hsing
陳炘毓
Chen, Shin Yu關鍵詞 類馬可夫鏈
存活分析
B型肝炎
第一次到達時間
國民生命表
semi-Markov chain
Survival analysis
HBV
First passage time
Life table日期 2010 上傳時間 8-Dec-2010 11:52:29 (UTC+8) 摘要 在此篇論文中，我們提出一個慢性Ｂ型肝炎病毒感染病程之數學模型。因為在病症間的轉移機率(Transition probability)是隨著患者的年齡變動，所以在過去的文獻中，已經有學者提出，在疾病轉移機率模型中，應加入國民生命表(Life table)，藉此讓機率模型更符合Ｂ型肝炎病患的生命歷程。但是過去的文獻中，學者並沒有利用加入國民生命表之後疾病模型做進一步的病程分析。在這篇論文當中，我們假設原始的疾病轉移模型是符合馬可夫鏈的性質，並且提出一種加入國民生命表的方法，賦予疾病有年齡相關特性之模型。根據文獻數據和類馬可夫機率性質，我們使用著名的Chapman-Kolmogorov公式計算Ｂ型肝炎的自然病程機率，並畫出病人的生存機率曲線(Survival curve)。文章最後將會藉由兩個例子來介紹此篇論文提出的模型。實驗數據結果證實，此模型不僅提供了一個更精確的方法去分析在病症與死亡間的轉移機率、平均餘命(Life expectancy)、以及在不同年齡的存活機率(Survival probability)，並且可以更進一步的分析且瞭解病情狀態之間的轉移狀況。
In this thesis, we propose a new mathematical model extending the natural history of hepatitis B virus (HBV) prognosis progression on chronic HBV infection. Since the actual transition probabilities between symptoms are dependent of ages, it has been proposed that the life table should be accommodated to the HBV prognosis progression model so that it can more properly explain the disease progression of the HBV patients. But in the literature, no further disease analysis and applications of it with the life table are discussed. In this thesis, we assume that the original disease progression is described by a Markov model, and propose a new method to combine the HBV progression with the life table so that the proposed model integrates data from the life table and allows the accommodation of age-dependent properties of the target disease. With clinical data based on annual incidence rates, the entire model is Semi-Markov based in nature. Computation methods similar to the celebrated Chapman-Kolmogorov equation can be applied to study the associated probability of each likely trajectory with desired initial ages and health states under the scenarios of natural history and various treatment policies. This method provides a more accurate way to analyze the transitions between symptoms, such as the mean life expectancy or the survival probabilities at different ages. We will give examples to demonstrate the proposed method in this thesis. Numerical results show the proposed model not only provides a more accurate method to analyze the mean life expectancy, the survival probabilities at different ages, and the transition probabilities from symptoms to death but also helps us to understand the transitions between symptoms.參考文獻 1. Anderson, P.K., Multistate models in survival analysis: A study of nephropathy and mortality in diabetes. Statistics in Medicine 7, pp. 661-670, 1988.
2. Bambha, K., and Kim, W.R., Cost-effectiveness analysis and incremental cost-effectiveness ratios: uses and pitfalls. European journal of gastroenterology and hepatology, vol. 16, no. 4, 2006.
3. Barbu, Vlad Stefan, Limnios, Nikolaos, Semi-Markov Chains and Hidden Semi-Markov Models toward Applications. Springer: New York, 2008.
4. Beck J.R, Pauker, S.G., The Markov process in medical prognosis. Medical Decision Making.1983; 3: 419-58.
5. Biase, G.D., D’Amico, G. Girolamo, A.D. Janssen, J. etc., A stochastic model for the HIV/AIDS dynamic evolution. Mathematical Problems in Engineering, pp. 1-14, 2007.
6. Bortolotti, F., Jara, P., Crivellaro, C., Hierro, L., Cadrobbi, P., Frauca, E., Camarena, C., De La Vega, A., Diaz, C., De Moliner L., and Noventa, F., Outcome of chronic hepatitis B in Caucasian children during a 20-year observation period. J. Hepatol. vol. 29, pp. 184-190, 1998.
7. Chu, C.J., Hussain , M., and Lok, A.S.F., Hepatitis B virus genotype B is associated with earlier HBeAg seroconversion compared to hepatitis B virus genotype C. Gastroenterology, vol. 122, pp. 1756-1762, 2002.
8. Chu, C.M., and Liaw, Y.F., Genotype C hepatitis B virus infection is associated with a higher risk of reactivation of hepatitis B and progression to cirrhosis than genotype B: A longitudinal study of hepatitis B e antigen-positive patients with normal aminotransferase levels at baseline. Journal of Hepatology, vol. 43, pp. 411-417, 2005.
9. Chu, C.M., Hung, S.J., Lin, J., Tai, D.I., and Liaw, Y.F., Natural history of hepatitis B e antigen to antibody seroconversion in patients with normal serum aminotransferase Levels. The American Journal of Medicine, vol. 116, pp. 829-834, 2004.
10. Cinlar, E., Introduction to Stochastic Processes. Prentice Hall: Englewood Cliffs, New Jersey, 1975.
11. Fattovich, G., Natural history and prognosis of hepatitis B. Seminar in Liver Disease, vol. 23, pp. 47-58, 2003.
12. Fattovich, G., Rugge, M., Brollo, L., Pontisso, P,. Noventa, F., Guido, M., Alberti, A., and Realdi, G., Clinical, virologic and histologic outcome following seroconversion from HBeAg to anti-HBe in chronic hepatitis type B. Hepatology, vol. 6, pp. 167-172, 1986.
13. Gambarin-Gelwan, M,. and Jacobson, I., Treatment of chronic hepatitis B infection,2007.www.gastro.org/.../Documents/08_Publications/06_GIHep_Annual_Review/Articles/GambarinGelwan-Jacobson.pdf.
14. Garber, A.M., Phelps, C.E., Economic foundations of cost-effectiveness analysis. Journal of Health Economics, vol. 17, pp. 1-31, 1997.
15. Hsu, Y.S., Chien, R.N., Yeh, C.T., Sheen, I.S., Chiou, H.Y., Chu, C.M., and Liaw, Y.F., Long-term outcome after spontaneous HBeAg seroconversion in patients with chronic hepatitis B. Hepatology, vol. 35, pp. 1522-1527, 2002.
16. Kay, R., A Markov model for analyzing cancer marker and disease states and survival studies. Biometrics 42, pp. 855-865, 1986.
17. Lefebvre, M. Applied Stochastic Process. Springer: New York, 2006.
18. Luh, P.H., and Phua, S. A cost-effective analysis for chronic Hepatitis B Virus with cirrhosis by discrete event simulation. ISPR Asia-Pacific Conference, pp. 64-65, Seoul, South Korea, 2008.
19. Liaw, Y.F., and Chu, C.M., “Hepatitis B virus Infection,” The Lancet, pp. 582-592, Feb., 2009.
20. Liaw, Y.F., Hepatitis B virus replication and liver and disease progression: the impact of antiviral therapy. Antiviral Theory, vol. 11, pp. 669-679, 2006.
21. Minitab , version 15, Minitab, Inc., University Park, USA, 2007.
22. Orito, E., Mizokami, M., Sakugawa, H., Michitaka, K., Ishikawa, K., Ichida, T., Okanoue, T., Yotsuyanagi, H., and Iino, S., A case-control study for clinical and molecular biological diffferences between hepatitis B viruses of genotype B and C. Japan HBV Genotype Research Group. Hepatology, vol. 33, pp. 218-223, 2001.
23. Pwu, R.F., and Chan, K.A., Cost-effectiveness analysis of interferon-alpha therapy in the treatment of chronic hepatitis B in Taiwan. J. Formosa Med. Assoc., vol. 11, pp. 632-41, 2002.
24. Ross, S.M., Introduction to probability models. Academic Press, M.A., 2003.
25. Russell, L.B., Gold, M.R., Siegel, J. E. Daniels, N. and Weinstein, M. C. The role of cost-effectiveness analysis in health and medicine. JAMA., vol. 276, no. 14, pp. 1172-1177, 1996.
26. Satten, G. A. and Sternberg, M.R., Fitting Semi-Markov models to interval-censored data with unknown initiation times. Biometrics, vol. 55, no. 2, pp. 507-513, 1999.
27. Sonnenberg, F.A., Beck J.R., Markov models in medical decision making: a practical guide. Medical Decision Making 1993, 13(4),pp. 322-38.
28. Sternberg, M.R., De Angelis, D., and Aalen, O.O., Bayesian back-calculation using a multi-state model with application to HIV. Statistics in Medicine, vol. 24, no. 24, pp. 3991-4007, 2005.
29. Taha, H.A., Operations Reaseach an introduction. Eighth edition, Pearson Edutacion, Inc.. 2003.
30. 行政院內政部統處,第九次(民國88~90年)臺灣地區國民生命表http://www.moi.gov.tw/stat/life.aspx
31. 行政院內政部統計處,簡易生命表函數定義及編算方法 http://www.moi.gov.tw/stat/life.aspx描述 碩士
國立政治大學
應用數學研究所
97751001
99資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097751001 資料類型 thesis dc.contributor.advisor 陸行 zh_TW dc.contributor.advisor Luh, Hsing en_US dc.contributor.author (Authors) 陳炘毓 zh_TW dc.contributor.author (Authors) Chen, Shin Yu en_US dc.creator (作者) 陳炘毓 zh_TW dc.creator (作者) Chen, Shin Yu en_US dc.date (日期) 2010 en_US dc.date.accessioned 8-Dec-2010 11:52:29 (UTC+8) - dc.date.available 8-Dec-2010 11:52:29 (UTC+8) - dc.date.issued (上傳時間) 8-Dec-2010 11:52:29 (UTC+8) - dc.identifier (Other Identifiers) G0097751001 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49457 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學研究所 zh_TW dc.description (描述) 97751001 zh_TW dc.description (描述) 99 zh_TW dc.description.abstract (摘要) 在此篇論文中，我們提出一個慢性Ｂ型肝炎病毒感染病程之數學模型。因為在病症間的轉移機率(Transition probability)是隨著患者的年齡變動，所以在過去的文獻中，已經有學者提出，在疾病轉移機率模型中，應加入國民生命表(Life table)，藉此讓機率模型更符合Ｂ型肝炎病患的生命歷程。但是過去的文獻中，學者並沒有利用加入國民生命表之後疾病模型做進一步的病程分析。在這篇論文當中，我們假設原始的疾病轉移模型是符合馬可夫鏈的性質，並且提出一種加入國民生命表的方法，賦予疾病有年齡相關特性之模型。根據文獻數據和類馬可夫機率性質，我們使用著名的Chapman-Kolmogorov公式計算Ｂ型肝炎的自然病程機率，並畫出病人的生存機率曲線(Survival curve)。文章最後將會藉由兩個例子來介紹此篇論文提出的模型。實驗數據結果證實，此模型不僅提供了一個更精確的方法去分析在病症與死亡間的轉移機率、平均餘命(Life expectancy)、以及在不同年齡的存活機率(Survival probability)，並且可以更進一步的分析且瞭解病情狀態之間的轉移狀況。 zh_TW dc.description.abstract (摘要) In this thesis, we propose a new mathematical model extending the natural history of hepatitis B virus (HBV) prognosis progression on chronic HBV infection. Since the actual transition probabilities between symptoms are dependent of ages, it has been proposed that the life table should be accommodated to the HBV prognosis progression model so that it can more properly explain the disease progression of the HBV patients. But in the literature, no further disease analysis and applications of it with the life table are discussed. In this thesis, we assume that the original disease progression is described by a Markov model, and propose a new method to combine the HBV progression with the life table so that the proposed model integrates data from the life table and allows the accommodation of age-dependent properties of the target disease. With clinical data based on annual incidence rates, the entire model is Semi-Markov based in nature. Computation methods similar to the celebrated Chapman-Kolmogorov equation can be applied to study the associated probability of each likely trajectory with desired initial ages and health states under the scenarios of natural history and various treatment policies. This method provides a more accurate way to analyze the transitions between symptoms, such as the mean life expectancy or the survival probabilities at different ages. We will give examples to demonstrate the proposed method in this thesis. Numerical results show the proposed model not only provides a more accurate method to analyze the mean life expectancy, the survival probabilities at different ages, and the transition probabilities from symptoms to death but also helps us to understand the transitions between symptoms. en_US dc.description.tableofcontents 謝辭 iAbstract ii中文摘要 iiiList of Figures ivList of Tables vi1 Introduction 12 A Life Table and Semi-Markov Chains 42.1 A Quick Review of A HBV Progression Model 42.2 Markov Chain 72.3 Chapman-Kolmogorov Equations 102.4 The Life Table 122.5 Markov Renewal Chains and Semi-Markov Chains 153 Model Structure 203.1 The Revised Life Table 203.2 The Construction of The Proposed Model 263.3 Computation Methods 314 Numerical Experiments and Analysis 345 Conclusion 69 Appendix 70 References 74 zh_TW dc.format.extent 5216247 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097751001 en_US dc.subject (關鍵詞) 類馬可夫鏈 zh_TW dc.subject (關鍵詞) 存活分析 zh_TW dc.subject (關鍵詞) B型肝炎 zh_TW dc.subject (關鍵詞) 第一次到達時間 zh_TW dc.subject (關鍵詞) 國民生命表 zh_TW dc.subject (關鍵詞) semi-Markov chain en_US dc.subject (關鍵詞) Survival analysis en_US dc.subject (關鍵詞) HBV en_US dc.subject (關鍵詞) First passage time en_US dc.subject (關鍵詞) Life table en_US dc.title (題名) 慢性B型肝炎病毒感染之年齡相關模型及存活機率分析 zh_TW dc.title (題名) An age-dependent model with survival analysis on chronic hepatitis b virus infection en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 1. Anderson, P.K., Multistate models in survival analysis: A study of nephropathy and mortality in diabetes. Statistics in Medicine 7, pp. 661-670, 1988. zh_TW dc.relation.reference (參考文獻) 2. Bambha, K., and Kim, W.R., Cost-effectiveness analysis and incremental cost-effectiveness ratios: uses and pitfalls. European journal of gastroenterology and hepatology, vol. 16, no. 4, 2006. zh_TW dc.relation.reference (參考文獻) 3. Barbu, Vlad Stefan, Limnios, Nikolaos, Semi-Markov Chains and Hidden Semi-Markov Models toward Applications. Springer: New York, 2008. zh_TW dc.relation.reference (參考文獻) 4. Beck J.R, Pauker, S.G., The Markov process in medical prognosis. Medical Decision Making.1983; 3: 419-58. zh_TW dc.relation.reference (參考文獻) 5. Biase, G.D., D’Amico, G. Girolamo, A.D. Janssen, J. etc., A stochastic model for the HIV/AIDS dynamic evolution. Mathematical Problems in Engineering, pp. 1-14, 2007. zh_TW dc.relation.reference (參考文獻) 6. Bortolotti, F., Jara, P., Crivellaro, C., Hierro, L., Cadrobbi, P., Frauca, E., Camarena, C., De La Vega, A., Diaz, C., De Moliner L., and Noventa, F., Outcome of chronic hepatitis B in Caucasian children during a 20-year observation period. J. Hepatol. vol. 29, pp. 184-190, 1998. zh_TW dc.relation.reference (參考文獻) 7. Chu, C.J., Hussain , M., and Lok, A.S.F., Hepatitis B virus genotype B is associated with earlier HBeAg seroconversion compared to hepatitis B virus genotype C. Gastroenterology, vol. 122, pp. 1756-1762, 2002. zh_TW dc.relation.reference (參考文獻) 8. Chu, C.M., and Liaw, Y.F., Genotype C hepatitis B virus infection is associated with a higher risk of reactivation of hepatitis B and progression to cirrhosis than genotype B: A longitudinal study of hepatitis B e antigen-positive patients with normal aminotransferase levels at baseline. Journal of Hepatology, vol. 43, pp. 411-417, 2005. zh_TW dc.relation.reference (參考文獻) 9. Chu, C.M., Hung, S.J., Lin, J., Tai, D.I., and Liaw, Y.F., Natural history of hepatitis B e antigen to antibody seroconversion in patients with normal serum aminotransferase Levels. The American Journal of Medicine, vol. 116, pp. 829-834, 2004. zh_TW dc.relation.reference (參考文獻) 10. Cinlar, E., Introduction to Stochastic Processes. Prentice Hall: Englewood Cliffs, New Jersey, 1975. zh_TW dc.relation.reference (參考文獻) 11. Fattovich, G., Natural history and prognosis of hepatitis B. Seminar in Liver Disease, vol. 23, pp. 47-58, 2003. zh_TW dc.relation.reference (參考文獻) 12. Fattovich, G., Rugge, M., Brollo, L., Pontisso, P,. Noventa, F., Guido, M., Alberti, A., and Realdi, G., Clinical, virologic and histologic outcome following seroconversion from HBeAg to anti-HBe in chronic hepatitis type B. Hepatology, vol. 6, pp. 167-172, 1986. zh_TW dc.relation.reference (參考文獻) 13. Gambarin-Gelwan, M,. and Jacobson, I., Treatment of chronic hepatitis B infection,2007.www.gastro.org/.../Documents/08_Publications/06_GIHep_Annual_Review/Articles/GambarinGelwan-Jacobson.pdf. zh_TW dc.relation.reference (參考文獻) 14. Garber, A.M., Phelps, C.E., Economic foundations of cost-effectiveness analysis. Journal of Health Economics, vol. 17, pp. 1-31, 1997. zh_TW dc.relation.reference (參考文獻) 15. Hsu, Y.S., Chien, R.N., Yeh, C.T., Sheen, I.S., Chiou, H.Y., Chu, C.M., and Liaw, Y.F., Long-term outcome after spontaneous HBeAg seroconversion in patients with chronic hepatitis B. Hepatology, vol. 35, pp. 1522-1527, 2002. zh_TW dc.relation.reference (參考文獻) 16. Kay, R., A Markov model for analyzing cancer marker and disease states and survival studies. Biometrics 42, pp. 855-865, 1986. zh_TW dc.relation.reference (參考文獻) 17. Lefebvre, M. Applied Stochastic Process. Springer: New York, 2006. zh_TW dc.relation.reference (參考文獻) 18. Luh, P.H., and Phua, S. A cost-effective analysis for chronic Hepatitis B Virus with cirrhosis by discrete event simulation. ISPR Asia-Pacific Conference, pp. 64-65, Seoul, South Korea, 2008. zh_TW dc.relation.reference (參考文獻) 19. Liaw, Y.F., and Chu, C.M., “Hepatitis B virus Infection,” The Lancet, pp. 582-592, Feb., 2009. zh_TW dc.relation.reference (參考文獻) 20. Liaw, Y.F., Hepatitis B virus replication and liver and disease progression: the impact of antiviral therapy. Antiviral Theory, vol. 11, pp. 669-679, 2006. zh_TW dc.relation.reference (參考文獻) 21. Minitab , version 15, Minitab, Inc., University Park, USA, 2007. zh_TW dc.relation.reference (參考文獻) 22. Orito, E., Mizokami, M., Sakugawa, H., Michitaka, K., Ishikawa, K., Ichida, T., Okanoue, T., Yotsuyanagi, H., and Iino, S., A case-control study for clinical and molecular biological diffferences between hepatitis B viruses of genotype B and C. Japan HBV Genotype Research Group. Hepatology, vol. 33, pp. 218-223, 2001. zh_TW dc.relation.reference (參考文獻) 23. Pwu, R.F., and Chan, K.A., Cost-effectiveness analysis of interferon-alpha therapy in the treatment of chronic hepatitis B in Taiwan. J. Formosa Med. Assoc., vol. 11, pp. 632-41, 2002. zh_TW dc.relation.reference (參考文獻) 24. Ross, S.M., Introduction to probability models. Academic Press, M.A., 2003. zh_TW dc.relation.reference (參考文獻) 25. Russell, L.B., Gold, M.R., Siegel, J. E. Daniels, N. and Weinstein, M. C. The role of cost-effectiveness analysis in health and medicine. JAMA., vol. 276, no. 14, pp. 1172-1177, 1996. zh_TW dc.relation.reference (參考文獻) 26. Satten, G. A. and Sternberg, M.R., Fitting Semi-Markov models to interval-censored data with unknown initiation times. Biometrics, vol. 55, no. 2, pp. 507-513, 1999. zh_TW dc.relation.reference (參考文獻) 27. Sonnenberg, F.A., Beck J.R., Markov models in medical decision making: a practical guide. Medical Decision Making 1993, 13(4),pp. 322-38. zh_TW dc.relation.reference (參考文獻) 28. Sternberg, M.R., De Angelis, D., and Aalen, O.O., Bayesian back-calculation using a multi-state model with application to HIV. Statistics in Medicine, vol. 24, no. 24, pp. 3991-4007, 2005. zh_TW dc.relation.reference (參考文獻) 29. Taha, H.A., Operations Reaseach an introduction. Eighth edition, Pearson Edutacion, Inc.. 2003. zh_TW dc.relation.reference (參考文獻) 30. 行政院內政部統處,第九次(民國88~90年)臺灣地區國民生命表http://www.moi.gov.tw/stat/life.aspx zh_TW dc.relation.reference (參考文獻) 31. 行政院內政部統計處,簡易生命表函數定義及編算方法 http://www.moi.gov.tw/stat/life.aspx zh_TW
