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·药物经济学·

药物经济学评价中Markov模型的周期内校正方法探讨 Δ

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沃 田 ，陈 磊，席晓宇（中国药科大学国家药物政策与医药产业经济研究中心，南京 211198）
中图分类号 R956 文献标志码 A 文章编号 1001-0408（2020）08-0980-05
DOI 10.6039/j.issn.1001-0408.2020.08.15

摘 要 目的：为减少药物经济学研究中Markov模型的误差提供参考。方法：参考国外相关文献，解释Markov模型误差产生的
原理，并介绍常用的半周期法、梯形法、Simpson’s 1/3 法、Simpson’s 3/8 法、生命表法及其在 Excel、TreeAge 软件中的实现方法。
结果与结论：Markov模型因离散化过程而产生误差，使用周期内校正方法可校正这一误差。半周期法是最常用的校正方法，是通
过增加第1周期一半的结果并减去最后1周期一半的结果进行校正；梯形法的校正是以区间首尾端点值的均值代表该区间，以直
角梯形的面积作为累计的结果；Simpson’s 1/3法和Simpson’s 3/8法则在梯形法的基础上在区间中插值并以插值点所在的连续曲
线代表整个曲线；寿命表法的校正中，生存人年数为该年龄组的组距与该年龄组和下一年龄组尚存人数的均值的乘积，生存人年
数则为各年龄组生存总人年数的总和。在Excel中，可根据方法原理设置函数来实现校正；而在TreeAge软件中，可通过设置Init
Rwd、Incr Rwd、Final Rwd的函数表达式来实现校正。在使用Markov模型进行药物经济学评价时，对于周期校正方法的选择，若
从建模的易用性、适用情形的广泛性等角度出发，建议使用梯形法；从结果的精确性角度出发，则建议使用Simpson’s 1/3 法，以提
高Markov模型的准确度。
关键词 药物经济学；Markov模型；周期内校正；半周期法；梯形法；Simpson’s 1/3 法；Simpson’s 3/8法；寿命表法

Discussion on Within-cycle Correction of Markov Model in Pharmacoeconomic Evaluation
WO Tian，CHEN Lei，XI Xiaoyu（Research Center of National Drug Policy & Ecosystem，China Pharmaceutical
University，Nanjing 211198，China）

ABSTRACT OBJECTIVE：To provide reference for reducing the error of Markov model in pharmacoeconomic evaluation.
METHODS：Referring to foreign literatures，the errors in Markov model were explained. The commonly used correction methods
were introduced：half-cycle correction，trapezoidal rule，Simpson’s 1/3 rule，Simpson’s 3/8 method and life table method and
their implementation in Excel and TreeAge software. RESULTS & CONCLUSIONS：The error of Markov model was caused by the
discretization process and could be corrected by the within-cycle correction methods. Half-cycle correction，was the most commonly
used correction method and could be corrected by adding half of the results of the first cycle and subtracting half of the results of
the last cycle. By trapezoidal rule，the interval was represented by the mean value of the first end point value of the interval，and
the area of right trapezoid was the cummulative result. Simpson’s 1/3 rule and Simpson’s 3/8 rule took another point in the interval
on the basis of trapezoidal correction and the continuous curve where these three points were represented the whole curve. By life
table method，the person-years of survival was the product of the group distance of the age group and the mean value of the
number of survivors of the age group and the next age group，and the total person-years of survival was the sum of person-years of
survival of each age group. In Excel，the fuction was set according to the method principle to realize the correction；in TreeAge
software，the function expression of Init Rwd，Inor Rwd and Final Rwd were set to realize the correction. When using Markov
model for pharmacoeconomic evaluation，if the selection of periodic correction method is based on the ease of modeling and the
universality of application，the trapezoid rule method is recommended；based on the accuracy of results，it is suggested to use
Simpson’s 1/3 method，so as to improve the accuracy of Markov model.
KEYWORDS Pharmacoeconomics；Markov model；Within-cycle correction；Semi-cycle correction；Trapezoidal rule；Simpson’s
1/3 rule；Simpson’s 3/8 rule；Life table method

药物经济学（Pharmacoeconomics）是为合理配置健 门组织的药品谈判中发挥了重要作用。药物经济学可
康资源而新兴的一门交叉学科，在近几年由国家医保部 分为基于临床数据的研究和基于模型的研究：其中，基
Δ 基金项目：国家社会科学基金重大项目（No.15ZDB167）；江苏 于临床数据的研究通过收集临床数据进行分析以判断
省教育厅2019年度高校哲学社会科学研究一般项目（No.2019SJA0062）； 药物的已知疗效和经济性；基于模型的研究则通过二手
中国药科大学“双一流”学科创新团队建设项目（No.CPU2018GY39） 数据、专家访谈等构建模型分析预测药物的疗效和经济
＊硕士研究生。研究方向：药物经济学。E-mail：cpuwotian@163.
性。目前药物经济学应用的主流模型包括：模拟群体层
com
面病程短且复杂程度低的静态决策树模型、模拟群体层
# 通信作者：讲师，博士。研究方向：药物经济学与医药卫生政
策。E-mail：cpuxixiaoyu@163.com 面病程长且复杂程度高的动态 Markov 模型、模拟个体

·980 · China Pharmacy 2020 Vol. 31 No. 8 中国药房 2020年第31卷第8期