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    Title: 由數學模型角度分析以抗病毒藥物降低罹患肝癌風險與其經濟效益
    Other Titles: Analysis on Minimizing the Risk of Hepatocellular Carcinoma with Antiviral Therapy and Its Cost-Effectiveness --- a Modeling Perspective
    Authors: 陳政輝
    Contributors: 應用數學學系
    Keywords: 慢性B型肝炎;抗病毒藥物;肝癌;肝功能指數
    Chronic Hepatitis B virus (HBV) infection;Antiviral Drugs;Hepatocellular Carcinoma(HCC);Alanine aminotransferase (ALT)
    Date: 2012
    Issue Date: 2016-04-19 11:41:39 (UTC+8)
    Abstract: 慢性B型肝炎由B型肝炎病毒所引起，在病毒長期活動並與宿主免疫反應作用之下，對肝臟造成了嚴重的傷害，病程後期亦可能引發肝癌，對患者健康與生命造成嚴重的威脅。根據近期醫學研究報告指出，患者血清中B型肝炎病毒DNA濃度高低為判斷患者罹癌之重要因子。當患者持續處於病毒DNA濃度高之狀態，其後續罹患肝癌之風險越高，反之，當患者之病毒DNA濃度越低，其後續罹患肝癌之風險亦較低。亦即，肝炎病毒活動愈頻繁，患者罹癌風險越高，因此，可預期若能有效抑制病毒活動，將可降低患者罹患肝癌之風險。 近年來，由於抗病毒藥物的發展，使得B型肝炎的治療有了長足的進步。值得一提的是，B型肝炎治療與抗病毒藥物的發展，得利於研究人員對愛滋病的研究。由於B型肝炎與愛滋病皆為病毒感染所引起，藉由增進對愛滋病毒 (HIV)之瞭解及比較兩種病毒間的相似性(或相異性)，亦增進對 HBV之瞭解。此外，B型肝炎抗病毒藥物常於研發抗愛滋病藥物時發現，或原為治療愛滋病之藥物。肝安能 (Lamivudine) 即為一最佳例子。此外，愛滋病治療經驗提供B型肝炎治療重要參考。在愛滋病治療中，除了抗藥性問題外，一個重要的考量為何時開始治療。若開始治療時間過早，除藥物可能毒性外，當病毒對多種藥物產生抗藥性時，在病程後期用藥選擇將受到極大限制。然而，若過晚用藥，在未施藥期間，病毒可能對患者造成永久性傷害。因此，目前愛滋病雖無法治癒，但若能選擇在適當時機以藥物介入，仍可控制病情，延長患者壽命。類比於愛滋病之治療，當B型肝炎患者免疫反應不足時(肝功能指數低於2倍正常上限者)，以抗病毒藥物治療效果不佳，且可能有抗藥性問題。然而，若不以抗病毒藥物介入治療，當患者病毒DNA濃度長期處於較高狀態時，其後續罹患肝癌之風險極高。因此，本研究探討當患者因免疫反應不足，在無法根治B型肝炎之情形下 (或達到e-抗原血清轉換 (HBeAg Seroconversion))，於適當時機以藥物介入，長期抑制病毒活動，以降低罹患肝癌風險的可能性。 本計畫延續計畫NSC 99-2221-E-004 -002 -MY2之慢性B型肝炎病程發展與治療問題，由數學模型著手，將最佳介入治療時機與對應之患者平均生存年限轉化為最佳化問題。藉由解答轉化後之問題，分析在患者可能發生急性症狀與抗藥性風險下，何時應以抗病毒藥物介入治療以延長患者平均生存年限。此外，以患者年平均醫療花費為基準，比較治療與否之經濟效益。而由於轉化後之最佳化問題為非凸性 (non-convexity)，具有多重局部最佳解 (local optimal solutions)，因此我們採用Trust-Tech 演算法求解。此一演算法可非隨機性(deterministically) 求取多個局部最佳解，由所得之局部最佳解中，選取最適解答，可增進對患者平均生存年限估算之準確度，以決定用藥與否及用藥最佳時機。 本計畫之研究成果將以表格呈現各模型參數與此長期使用抗病毒藥物治療可行與否之關聯性，讓醫師除對患者情形由醫學角度作考量外，亦可由文獻和現有臨床資料為輔，判斷患者是否與何時需用藥。此外，本計畫所提出之數學模型將建置為模擬軟體，未來新研發之抗病毒藥物與其抗藥性資訊可用此軟體分析，提供最新相關訊息，供臨床醫師與醫學專家參考。
    Chronic hepatitis B (CHB) is caused by the infection of hepatitis B virus (HBV). The complex interaction between virus and host’s immune response results in severe damage to the liver. It could also lead to hepatocellular carcinoma (HCC) and henceforth imposes great threatens to patients’ life. According to recent medical reports, patients’ persistence in the state of high circulating HBV DNA level is an important predictor to their development of HCC. The higher the DNA level is, the greater the risk of the development of HCC will be. This demonstrates that the activeness of the virus is significantly related to the occurrence of HCC. Therefore, it is expected that effective viral suppression will lead to reduction of the incidence of HCC. Significant progress has been made to the treatment of CHB due to the recent invention of antiviral drugs. It is worth mentioning that this progress benefits a lot from the research of Acquired Immune Deficiency Syndrome (AIDS). Both diseases are caused by the infection of viruses. Through the study of human immunodeficiency virus (HIV), researchers gain better understanding to HBV by exploring its similarity and distinction compared with HIV. Meanwhile, many antiviral drugs in treating CHB are the byproducts of the development of antiviral drugs of AIDS or they can also be used to treat AIDS. Furthermore, lessons learned from treating AIDS provide valuable experiences in treating CHB. Especially, in the AIDS treatment problem, one important concern is the optimal initiation time of the drug interventions. Early treatment will restrict patients’ future treatment options in later course especially when drug resistance presents. On the other hand, when late treatment policy is applied, patients are exposed to the risk of irreversible damage due to HIV. Therefore, when the optimal initiation time of treatment can be properly determined, drug interventions can effectively delay the disease progression and can prolong patients’ life even though the HIV can’t be completely eradicated. Similar situations occur in treating CHB patients with insufficient immune response. (i.e. Alanine aminotransferase (ALT) level is less than 2 times of the upper limit of normal reference.) The efficacy of antiviral therapy is unsatisfactory and patients hardly reach the state of HBeAg seroconversion. However, optimal initiation of the treatment with long-term follow-up viral suppression can still minimize the risk of later development of HCC even though the HBV can’t be completely eradicated. Therefore, it has potential to prolong patients’ life. The major focus of this project proposal is to explore the feasibility of such a long-term antiviral therapy. This project continues and extends the study of NSC 99-2221-E-004 -002 -MY2 on the disease progression modeling and the treatment of CHB. The long-term antiviral treatment process is formulated as nonlinear optimization problem. Its solution provides the answers to the optimal initiation time of the antiviral treatment policy and the resulting patients’ life expectancy. When the life expectancy serves the criteria of treatment efficacy, the result assists the decision of when and whether this treatment should be implemented. The cost-effectiveness of the long-term treatment policy can be studied accordingly. Due to the non-convexity property, the formulated optimization problem may possess multiple local optimal solutions. To overcome this difficulty, Trust-Tech algorithm is applied in solving the formulated problem. This algorithm can deterministically locate multiple local optimal solutions. Among the obtained solutions, the best solution can be chosen to improve the estimation of patients’ life expectancy. It leads to better decision of when and whether the treatment should be implemented, Various parameters of the proposed model and their relation to the feasibility of the long-term antiviral therapy will be presented as a table. It will be important complementary information that assists clinic practitioners to decide whether a targeted patient can benefit from this long-term therapy. Meanwhile, the developed mathematical model will be realized as a simulation tool. When future antiviral drugs and their resistance profiles are available, they could be analyzed with the tool to provide up-to-date information to clinic practitioners and medical specialists.
    Relation: 計畫編號 NSC 101-2221-E004-003
    Data Type: report
    Appears in Collections:[Department of Mathematical Sciences] NSC Projects

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