乙型肝炎防治经济学评价——马尔科夫模型的构建

Development of Markov models for economics evaluation of strategies on hepatitis B vaccination and population-based antiviral treatment in China

目的构建乙型肝炎（乙肝）防治经济学评价马尔科夫模型。方法依据马尔科夫链理论和方法，参考国内外相关文献，采用Tree Age Pro2015软件构建不同特征及不同乙肝防治人群的马尔科夫模型（包括各种状态及其链接的设置、状态概率的确定），并对该模型进行验证。结果建立了新生儿乙肝免疫预防马尔科夫模型、围产期HBV感染后转归马尔科夫模型、成年人乙肝免疫预防马尔科夫模型、慢性乙肝抗病毒治疗和一般人群马尔科夫5类模型。新生儿模型是基础，包含10个Markov状态，分别为乙肝易感、免疫耐受、免疫清除、低复制、再活动、HBsAg清除、代偿和失代偿性肝硬化、肝细胞癌和死亡。围产期模型不包含乙肝易感，成年人模型忽略免疫耐受，均为9个Markov状态，一般人群马尔科夫模型只有健康和死亡2个Markov状态。5类模型共有起始状态9个，引入起始概率；Markov状态之间的转移概率共27个，根据我国乙肝防治现状确定。模拟验证显示，本研究构建的乙肝防治马尔科夫模型符合我国当前实际。结论马尔科夫模型结构和参数具有动态不确定性，本研究构建的模型可以满足我国乙肝防治策略经济学评价需求。

Objective To construct the Markov models to reflect the reality of prevention and treatment interventions against hepatitis B virus （HBV） infection, simulate the natural history of HBV infection in different age groups and provide evidence for the economics evaluations of hepatitis B vaccination and population-based antiviral treatment in China. Methods According to the theory and techniques of Markov chain, the Markov models of Chinese HBV epidemic were developed based on the national data and related literature both at home and abroad, including the settings of Markov model states, allowable transitions and initial and transition probabilities. The model construction, operation and verification were conducted by using software TreeAge Pro 2015. Results Several types of Markov models were constructed to describe the disease progression of HBV infection in neonatal period, perinatal period or adulthood, the progression of chronic hepatitis B after antiviral therapy, hepatitis B prevention and control in adults, chronic hepatitis B antiviral treatment and the natural progression of chronic hepatitis B in general population. The model for the newborn was fundamental which included ten states, i.e. susceptiblity to HBV, HBsAg clearance, immune tolerance, immune clearance, low replication, HBeAg negative CHB, compensated cirrhosis, decompensated cirrhosis, hepatocellular carcinoma （HCC） and death. The susceptible state to HBV was excluded in the perinatal period model, and the immune tolerance state was excluded in the adulthood model. The model for general population only included two states, survive and death. Among the 5 types of models, there were 9 initial states assigned with initial probabilities, and 27 states for transition probabilities. The results of model verifications showed that the probability curves were basically consistent with the situation of HBV epidemic in China. Conclusion The Markov models developed can be used in economics evaluation of hepatitis B vaccination and treatment for the elimination of HBV infection in China though the structures and parameters in the model have uncertainty with dynamic natures.