Eichner M, Diebner H H, Schubert C, Kreth H W, Dietz K
Department of Medical Biometry, Eberhard-Karls-University, Westbahnhofstr. 55, D-72070 Tübingen, Germany.
Stat Med. 2002 Aug 30;21(16):2355-68. doi: 10.1002/sim.1043.
We present a method to estimate the time-dependent vaccine efficacy from the cohort-specific vaccination coverage and from data on the vaccination status of cases and apply it to a measles epidemic in Germany which involved 529 cases, 88 of whom were vaccinated and 370 unvaccinated (for the remaining 71 cases the vaccination status is unknown). Our epidemiological model takes into account that maternal antibodies prevent successful vaccination and that vaccine immunity may be lost over time. Model parameters are estimated from the data using maximum likelihood. Vaccination coverage, as determined in school surveys, ranged from 27.6 per cent for the cohort born in 1974 to 85 per cent for the 1986 cohort, which is far too low to prevent measles transmission. Cohorts for which no school surveys were performed are omitted from analysis. Thus, sufficient data are available for only 282 cases, 69 of whom are vaccinated. According to our estimates, measles vaccinations provided no immunity before 1978 (95 per cent CI: 0 to 47 percent), for the period 1978-1982, the estimated vaccine efficacy was 80 percent (95 percent CI: 67 to 89 percent), and for 1982-1990 it was 97 percent (95 percent CI: 93 to 99 percent). After 1990, the estimated value dropped to 89 per cent, but its confidence interval widely overlaps with that of the previous period (95 percent CI: 74 to 97 percent). Loss of immunity was estimated to be zero (95 percent CI: 0 to 0.003/year). Several sensitivity analyses were performed with respect to the model assumptions. A modified model which assumed constant efficacy at all vaccination times yielded a high estimate of 96 per cent (95 percent CI: 92 to 98 percent) for primary vaccine efficacy but also a high loss rate of immunity of 0.007/year (95 percent CI: 0.001 to 0.012) to explain the high fraction of vaccinated cases among older individuals. The likelihood score value is however significantly inferior compared to the score value of the model with time-dependent vaccine efficacy.
我们提出了一种方法，可根据特定队列的疫苗接种覆盖率以及病例的疫苗接种状态数据来估计随时间变化的疫苗效力，并将其应用于德国的一场麻疹疫情，该疫情涉及529例病例，其中88例接种了疫苗，370例未接种（其余71例病例的疫苗接种状态未知）。我们的流行病学模型考虑到母体抗体可阻止疫苗接种成功，且疫苗免疫力可能会随时间丧失。使用最大似然法从数据中估计模型参数。根据学校调查确定的疫苗接种覆盖率，1974年出生队列的覆盖率为27.6%，1986年队列的覆盖率为85%，这远低于预防麻疹传播所需的水平。未进行学校调查的队列被排除在分析之外。因此，仅282例病例有足够的数据，其中69例接种了疫苗。根据我们的估计，1978年之前麻疹疫苗接种未产生免疫力（95%置信区间：0至47%），1978 - 1982年期间，估计疫苗效力为80%（95%置信区间：67至89%），1982 - 1990年为97%（95%置信区间：93至99%）。1990年之后，估计值降至89%，但其置信区间与前一时期有很大重叠（95%置信区间：74至97%）。估计免疫力丧失率为零（95%置信区间：0至0.003/年）。针对模型假设进行了多项敏感性分析。一个修改后的模型假设在所有疫苗接种时间的效力恒定，其对初次疫苗效力的估计值较高，为96%（95%置信区间：92至98%），但免疫力丧失率也较高，为0.007/年（95%置信区间：0.001至0.012），以解释老年个体中接种疫苗病例的高比例。然而，与具有随时间变化疫苗效力的模型的得分值相比，似然得分值明显更低。
