摘要
目的建立数学模型预测乙型肝炎疫苗(HepB)、风疹减毒活疫苗(RV)和麻疹减毒活疫苗(MV)接种后的抗体衰减趋势。方法用曲线拟合的方法,对国产HepB、RV和MV接种后抗体水平(?)随时间(X)的实测数据拟合数学模型,经拟合优度检验,验证模型的可靠性。结果拟合的HepB、RV和MV接种后抗体衰减模型分别为?=165.67exp(-0.019X)、?=269.39e~(-0.3603X)-61.26、?=90.95X~(-0.61),模型决定系数R~2分别为0.98、0.95和1.00,预测误差分别为0.02、0.05、0.003。结论用曲线拟合法拟合HepB、RV和MV接种后抗体衰减趋势的适配性较好。
Objective To develop mathematical models to predict antibody levels after vaccination with hepatitis B vaccine(HepB),rubella attenuated live vaccine(RV), and measles attenuated live vaccine(MV). Methods We used a curve fitting method to develop mathematical models based on actual antibody levels(?) over time(X) after vaccination with domestic HepB, RV, and MV; we determined reliability using the goodness-of-fit test. Results The fitted models for HepB, RV, and MV were ?=165.67 exp(-0.019 X),?=269.39 e~(-0.3603 X)-61.26, and ?=90.95 X~(-0.61), respectively; coefficients of determination(R~2) were 0.98, 0.95, and 1.00, with prediction errors of 0.02, 0.05, and 0.003, respectively. Conclusion Models developed with a curve fitting method reliably predicted antibody levels after vaccination with HepB, RV, and MV.
引文
[1]罗凤基,赵伟,张菁.麻疹减毒活疫苗抗体衰减趋势的幂曲线模型拟合及抗体持久性预测研究[J].中国计划免疫,2007,13(2):130-131.LUO Fengji,ZHAO Wei,ZHANG Jing.Study on the establishment power curve model of antibody attenuation trend of the measles live vaccine and prospect for the antibody permanence of the vaccine by model[J].Chinese Journal of Vaccines and Immunization,2007,13(2):130-131.
[2]曹传昭.成人乙型肝炎疫苗初次免疫5年后免疫持久性随访研究[D].济南:山东大学,2016.CAO Chuanzhao.Antibody levels and immune memory persistence af ter primary vaccination with three doses hepatitis B vaccine among adults:a 5-year follow-up study[D].Jinan:Shandong University,2016.
[3]孔青.成人不同免疫程序接种乙肝疫苗12年后体液免疫持久性比较研究[D].济南:山东大学,2018.KONG Qing.Antibody persistence of hepatitis B vaccine among adults by dif ferent immunization schedules:a twelve-year comparat ive study[D].Jinan:Shandong University,2018.
[4]黄跃龙,李树民,唐蕊妍,等.国产冻干风疹减毒活疫苗免疫持久性研究[J].中国自然医学杂志,2004,6(2):84-85.HUANG Yuelong,LI Shumin,TANG Ruiyan,et al.Study on the immunity duration of the lyophilized attenuated live rubella vaccine[J].Chinese Journal of Natural Medicine,2004,6(2):84-85.
[5]徐福根,姚怀芳,蒋金香,等.BRDⅡ株风疹减毒活疫苗接种10~11年后的免疫持久性[J].中国计划免疫,1998,4(3):147-150.XU Fugen,YAO Huai fang,J IANG J inxiang,et al.Persistence of antibody 10-11 years af ter vaccination with BRDⅡstrain live attenuated rubella vaccine[J].Chinese Journal of Vaccines and Immunization,1998,4(3):147-150.
[6]王树巧,陈志慧,谢广中,等.麻疹疫苗免疫持久性研究-初免后24-25年追踪观察[J].中国生物制品学杂志,2002,15(1):58-60.WANG Shuqiao,CHEN Zhihui,XIE Guangzhong,et al.Persistence oflive measles vaccine 24-25 years af ter primary immunization[J].Chinese Journal of Biologicals,2002,15(1):58-60.
[7]周洋.肠道病毒71型灭活疫苗免疫持久性及模型预测研究[D].南京:东南大学,2016.ZHOU Yang.The persistence of neutralizing antibodies induced by enterovirus 71 vaccine and predicted by model[D].Nanjing:Southeast University,2016.
[8]倪宗瓒.医学统计学[M].第2版,北京:人民卫生出版社,1995:112-116.NI Zongzan.Medical stat ist ics[M].Second edit ion.Beijing:People's Medical Publishing House,1995:112-116.
[9]孙振球.医学统计学[M].第3版,北京:人民卫生出版社,2013:169-173.SUN Zhenqiu.Medical stat ist ics[M].Third edit ion.Beijing:People's Medical Publishing House,2013:169-173.
[10]罗凤基,董春明,沈永刚,等.指数模型拟合法在乙型肝炎疫苗接种后抗体持久性预测中的应用[J].中华流行病学杂志,2004,25(9):805-807.LUO Fengji,DONG Chunming,SHEN Yonggang,et al.Application of exponent curve model to study the hepatitis B DNA recombinant yeast derived vaccine antibody levels[J].Chinese Journal of Epidemiology,2004,25(9):805-807.