HBV Infection Prognosis Prolonged Simulation Models
5. The Outcome of DES Model
5.2 DES versus Markov
In this section, we compare the results of a DES model and a Markov model for chronic HBV disease progression. The results are based on assuming that the patients are at state s1 starting at age 25. Table 3 represents the outcome of a DES model and Table 4 shows the result of a Markov model.
Table 3: The simulated disease progression probabilities distribution for a DES model
States Ages
s1 s2 s3 s4 s5 s6 s7 s8 s9 s10
25 1 0 0 0 0 0 0 0 0 0
30 0.4864 0.3059 0.0308 0.0130 0.1104 0.0306 0.0061 0.0044 0.0072 0.0054 35 0.1452 0.4126 0.0177 0.0367 0.1814 0.1028 0.0308 0.0200 0.0312 0.0221 40 0.1448 0.4126 0.0177 0.0367 0.1814 0.1030 0.0308 0.0196 0.0312 0.0221 45 0.0065 0.2146 0.0007 0.0623 0.1273 0.1667 0.1137 0.0570 0.0877 0.1637 50 0.0036 0.1202 0.0006 0.0540 0.0931 0.1426 0.1534 0.0590 0.0872 0.2872 55 0.0005 0.0135 0.0002 0.0340 0.0425 0.0699 0.2054 0.0410 0.0562 0.5370 60 0.0001 0.0023 0 0.0231 0.0327 0.0381 0.2094 0.0273 0.0349 0.6320
65 0 0.0007 0 0.0148 0.0266 0.0181 0.2014 0.0159 0.0187 0.7039
70 0 0.0003 0 0.0091 0.0221 0.0093 0.1814 0.0094 0.0091 0.7593
75 0 0.0002 0 0.0056 0.0188 0.0047 0.1497 0.0049 0.0040 0.8122
80 0 0.0001 0 0.0040 0.0141 0.0023 0.1101 0.0025 0.0019 0.8659
Table 4: The simulated disease progression probabilities distribution for a Markov model
States Ages
s1 s2 s3 s4 s5 s6 s7 s8 s9 s10
25 1 0 0 0 0 0 0 0 0 0
30 0.4479 0.3275 0.0263 0.0096 0.1379 0.0289 0.0034 0.0047 0.006 0.0078 35 0.201 0.3948 0.0118 0.0185 0.2075 0.076 0.0173 0.0166 0.0158 0.0407 40 0.09 0.3639 0.0053 0.0233 0.225 0.1044 0.0367 0.0279 0.0218 0.1017 45 0.0401 0.3031 0.0024 0.0251 0.2206 0.1122 0.0578 0.0345 0.0234 0.1808 50 0.0178 0.2399 0.001 0.0249 0.2072 0.106 0.0778 0.0363 0.0222 0.2669 55 0.0078 0.1841 0.0005 0.0237 0.1901 0.0926 0.0952 0.0343 0.0194 0.3524 60 0.0034 0.1375 0.0002 0.0217 0.1707 0.0763 0.1086 0.0299 0.016 0.4358 65 0.0015 0.1 0.0001 0.0193 0.15 0.0599 0.1171 0.0245 0.0126 0.5151 70 0.0006 0.07 0 0.0164 0.1272 0.0447 0.1187 0.0189 0.0094 0.5941 75 0.0002 0.0463 0 0.0133 0.1022 0.0312 0.1119 0.0134 0.0066 0.6748 80 0.0001 0.0282 0 0.0098 0.0755 0.0199 0.0955 0.0087 0.0042 0.7582
13 Table 3 and Table 4 show the simulated disease progression probabilities distribution. After ten years, about 14.52% it will be in s1 and 18.14% in s5, and 2.2% in s10 in a DES model, whiles about 9%
it will be in s1 and 20.75% in s5, and 4% in s10 in a Markov model. Likewise, the other probabilities can be interpreted in the same manner. Figure 6 and Figure 7 show the corresponding survival probability simulated from a DES and a Markov model respectively. Moreover, the remaining life expectancy for DES model and Markov model are 36.31 years and 39.48 years.
Figure 6: The survival probability of different ages starting at age 25
Figure 7: The survival probability of different ages starting at age 25
20 30 40 50 60 70 80 90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Age
Probability
20 30 40 50 60 70 80 90 100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
14
6. Conclusion
A model of DES is a tool for decision support system. The key feature of any decision model is to be “fit for purpose” for decision-making[25]. A model is a logic mathematical framework that permits the integration of facts and values and that links these data to outcomes for decision makers. If a model built at human disease processes to reasonably inform decision-makers and deal with uncertainty, variability, and heterogeneity, interaction, etc., simulation can appropriately handle the realities to correctly model it at the required depth, although it may involve a large number of computations which may be a hindrance to conducting DES. However, as computing techniques emerge dramatically, DES becomes easy and powerful for various managerial purposes.
Our analysis has two strengths. First, to our knowledge, our study is the first discrete event simulation model of decision analysis to compare competing strategies for chronic HBV infection.
Previous models have focus on either the Markov model or decision tree analysis. Second, our model acknowledges the increasing prevalence of simulation models. This approach increases the generalizability of modeling flexibility in light of statistical data.
Our study only demonstrates a possible construction for a DES used in analysis of chronic HBV.
Our model has several limitations. First, several of our estimates are based on literature which may depend on different design, patient population, follow-up and quality. Our estimates of patient health preferences may be limited because we adopted utilities for cirrhosis health states in HBV from limited sources. However, it is reasonable to assume that a patient who develops cirrhosis or related complications would have the same quality of life decrement regardless of time. Second, the time period of health states were estimated and adjusted accordingly to systematical consistence of simulation. More conditional health statuses could be included for better results and decision-making processes.
7. Acknowledgements
The authors wish to thank Dr. Y.F. Liaw for valuable comments in treatments for CHB, Mr. Y.
Samyshkin in modelling, and IMS Health in supporting Mr. N. Wang and K. Sun in programming for this work.
References
1. Bortolotti F, Jara P, Crivellaro C, Hierro L, Cadrobbi P, Frauca E, Camarena C, De La Vega A, Diaz C, De Moliner L, Noventa F. Outcome of chronic hepatitis B in Caucasian children during a 20-year observation period. J Hepatol 1998; 29: 184-190.
2. Brennan A, Chick SE, Davis R. A taxonomy of model structures for economic evaluation of health technologies Health Economics 15: 1295-1310 2006.
3. Caro JJ, Möller J, Getsios D., Discrete Event Simulation: The Preferred Technique for Health Economic Evaluations? Value Health. 2010 Dec; 13(8):1056-60.
4. Caro JJ., Pharmacoeconomic analyses using discrete event simulation, Pharmacoeconomics,
15 2005:23(4), 323-332.
5. Chen CH, Chen YY, Chen GH, Yang SS,Tang HS, Lin HH, Lin DY, Lo SK, Du JM, Chang TT, Chen SC, Liao LY, Kuo CH, Lin KC, Tai DI, Changchien CS, Chang WY, Sheu JC, Chen DS, Liaw YF, Sung JL. Hepatitis B virus transmission and epatocarcinogenesis: a 9 year retrospective cohort of 13 676 relatives with hepatocellular carcinoma. Journal of Hepatology 2004; 40:
653-659.
6. Chu CJ, Hussain M, Lok ASF. Hepatitis B virus genotype B is associated with earlier HBeAg seroconversion compared to hepatitis B virus genotype C. Gastroenterology 2002; 122: 1756-1762.
7. Chu CM, Hung SJ, Lin J, Tai DI, Liaw YF. Natural history of hepatitis B e antigen to antibody seroconversion in patients with normal serum aminotransferase Levels. The American Journal of Medicine 2004; 116: 829-834.
8. Chu CM, Liaw YF. 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 2005; 43: 411-417.
9. Chu CM, Liaw YF. Hepatitis B virus-related cirrhosis: natural history and treatment. Seminars in Liver Disease 2006; 26 (2): 142-152.
10. Eldabi T, Paul RJ, Young T. Simulation modeling in healthcare: reviewing legacies and investigating futures. Journal of the Operational Research Society 2007; 58, 262-270.
11. Fattovich, G. Natural history and prognosis of hepatitis B. Seminar in Liver Disease 2003 Feb;23(1):47-58.
12. Fattovich G, Rugge M, Brollo L, Pontisso P, Noventa F, Guido M, Alberti A, Realdi G. Clinical, virologic and histologic outcome following seroconversion from HBeAg to anti-HBe in chronic hepatitis type B. Hepatology 1986; 6: 167-172.
13. Gambarin-Gelwan M, Jacobson I. Treatment of chronic hepatitis B infection, 2007;
www.gastro.org/.../Documents/08_Publications/06_GIHep_Annual_Review/Articles/GambarinGel wan-Jacobson.pdf.
14. Hsu YS, Chien RN, Yeh CT, Sheen IS, Chiou HY, Chu CM, Liaw YF. Long-term outcome after spontaneous HBeAg seroconversion in patients with chronic hepatitis B. Hepatology 2002; 35:
1522-1527.
15. Katsaliaki K, Mustafee N. Applications of simulation within the healthcare context, Journal of the Operational Research Society 2011; 62, 1431-1451.
16. Liaw YF. Hepatitis B virus replication and liver and disease progression: the impact of antiviral therapy. Antiviral Theory 2006; 11: 669-679.
17. Matlab, Version R2008b, The MathWorks, Inc., USA, 2008.
18. M.H. AI Yousef, Estimation of Parameters and Truncation Point for the Truncated Gompertz Distribution, J. of King Saud Univ., Vol. 5, Admin Sci. (2), 35-48.
19. Orito E, Mizokami M, Sakugawa H, Michitaka K, Ishikawa K, Ichida T, Okanoue T, Yotsuyanagi H, 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 2001; 33:
218-223.
20. ProModel software 4.1 (Promodel Co.), 2001.
21. Pwu RF, Chan KA. Cost-effectiveness analysis of interferon-alpha therapy in the treatment of chronic hepatitis B in Taiwan, J Formos Med Assoc 2002;101:632-41.
22. Taiwan life table (1999-2001), Department of Statistics, Ministry of the Interior of Taiwan.
http://www.moi.gov.tw/stat/life.aspx
16 23. The analysis of the main cause of death in Taiwan, 2011. Department of Health, Executive Yuan,
R.O.C.,http://www.doh.gov.tw/CHT2006/DM/DM2_2.aspx?now_fod_list_no=11962&class_no=4 40&level_no=4
24. TreeAge Pro Suite 2009, version 2009, TreeAge Software, Inc., 2009.
25. Weinstein MC, O'Brien B, Hornberger J, Jackson J, Johannesson M, McCabe C, Luce BR, Principles of good practice for decision analytic modeling in health-care evaluation: report of the ISPOR Task Force on Good Research Practices--Modeling Studies, Value in Health, 2003, 6(1), 9-16.
26. Yeh CT, Sheen IS, Chen TC, Hsien SY, Chu CM, Liaw YF. Prednisolone modulates the therapeutic effect of interferon to eliminate preferentially the hepatitis B virus precore stop mutant.
Journal of Hepatology 2000; 32:829-836.
27. Y. F. Liaw and C. M. Chu, “Hepatitis B virus Infection,” The Lancet, Vol.373, No.9663, 582-592, Feb., 2009.
17
Appendix
A Chronic Hepatitis B Virus Infection Model on TreeAge
We use the software TreeAge [24] as a computing tool to compare results of the HBV disease progression with that calculated by the proposed model in this paper. The Markov model in TreeAge [24] is shown as a tree in Figure A. The transitional probabilities between symptoms are defined in the first box of the tree based on Figure 2. For each Markov node, first it will decide that whether or not the patient will die by population mortality or disease progression. If the patient died, then the disease progression will end up with death; if the patient does not die of population mortality, then the patient will make a transfer to another state or simply stay at the previous state. In Figure A, the symbols pDie, pDieDecompensation, and pDieHCC represent the population mortality, the probabilities of death at state decompensation and at state HCC respectively. Besides, pDNA1067_DNA1045 means the transitional probability from state “HBeAg(+) hepatitis HBV-DNA >2 10 6 ~ 7IU/ml” to “HBeAg(+) hepatitis HBV-DNA>2 10 4 ~ 5IU/ml”. The interpretations for the other transition probabilities are similar. The symbol “#” represents the probability of one subtracting the total probabilities of other transitions above. Note in the first block named “HBV problem”, pDie is defined to be that calculated by one subtracting the survival probability in the life table at different ages.
18 Figure A: The HBV disease progression model in TreeAge.
The survival probability at different ages in Table A is applied to the Markov model with TreeAge as well. Table A shows the simulated disease progression probabilities distribution, which is similar to the result in Table A. The simulated disease progression probability distributions are plotted in Figure B.
Moreover, the corresponding survival probability can be computed simultaneously. Figure D shows the
19 survival curve for the patients infected HBV starting at age 25.
Table A: The simulated disease progression probabilities distribution by using TreeAge
States
Ages s1 s2 s3 s4 s5 s6 s7 s8 s9 s10
25 1 0 0 0 0 0 0 0 0 0
30 0.4478 0.3274 0.0263 0.0087 0.1378 0.0298 0.0034 0.0047 0.0060 0.0081 35 0.2009 0.3946 0.0118 0.0148 0.2063 0.0795 0.0174 0.0169 0.0162 0.0417 40 0.0899 0.3635 0.0053 0.0170 0.2216 0.1100 0.0371 0.0287 0.0225 0.1046 45 0.0400 0.3024 0.0023 0.0171 0.2142 0.1189 0.0582 0.0358 0.0243 0.1867 50 0.0177 0.2392 0.0010 0.0161 0.1975 0.1130 0.0782 0.0378 0.0232 0.2763 55 0.0078 0.1831 0.0005 0.0146 0.1773 0.0991 0.0953 0.0358 0.0203 0.3662 60 0.0034 0.1363 0.0002 0.0129 0.1554 0.0820 0.1080 0.0314 0.0168 0.4537 65 0.0014 0.0986 0.0001 0.0110 0.1328 0.0646 0.1154 0.0258 0.0132 0.5371 70 0.0006 0.0684 0.0001 0.0091 0.1091 0.0482 0.1155 0.0198 0.0099 0.6197 75 0.0002 0.0447 0.0000 0.0070 0.0844 0.0336 0.1069 0.0140 0.0068 0.7023 80 0.0001 0.0265 0.0000 0.0050 0.0595 0.0212 0.0888 0.0089 0.0043 0.7857
Figure B: Starting from s1, the simulated disease progression with probabilities at different states by using TreeAge
20 Figure C: The survival curve starting from s1 computed by using TreeAge
6
科技部補助專題研究計畫出席國際學術會議心得報告
日期： 年 月 日
一、參加會議經過
林蔚君博士是INFORMS 美國作業研究和管理科學會的國際部的負責人，她希望為臺灣同 時也為INFORMS 努力創造更多的國際聯繫，因此計畫在 INFROMS 的 2014 年會中推銷兩份臺灣 主導的國際期刊Journal of industrial and production engineering (JIPE) 和 International Journal of Operations Research (IJOR)，期待增加更多的學術影響力。於是由張國晧教授、林東盈教授、王逸 琳教授和我組織一個場次，特別報告臺灣相關的學術論文。
這是一個超大型的學術會議，據主辦單位估計有將近5500 人參加這個會議，會議共舉行四 天。我們的場次在星期一，參加的人除了對論文主題有興趣的人外，也包括幾位來自歐洲、南美 洲、北美洲、亞洲和非洲等國際學術期刊的主要編輯，他們對我們的期刊和論文都給予肯定，也 希望INFORMS 的期刊可以與我們的期刊作更多的互動，給我們很多的建議。
林蔚君博士在會後也邀請國際期刊的編輯和部份INFORMS 國際部的成員開會討論增加互 動的具體作法，希望能為新進人員和博士生製造更多的曝光機會。
因為臺灣已經成立INFORMS Taiwan chapter，我和王逸琳教授參加 Chapters 的早餐會，我 們代表臺灣和其他的成員交換工作經驗，也為國際人士介紹臺灣相關的學術以及學生活動。