Estimation of the time‐dependent vaccine efficacy from a measles epidemic

Abstract

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.

The Effects of Regional Vaccination Heterogeneity on Measles Outbreaks with France as a Case Study

“…The high end of the range is in the case where two MMR doses are administered as recommended. Most of the literature focusing on efficacy in Europe [11,26,16] suggest an accurate range to fall between 92% and 96% nationwide. We opted to consider efficacy as 95% with coverage between 84% and 94%.…”

Effectiveness assessment of vaccination policy against measles epidemic in Japan using an age–time two-dimensional mathematical model

“…Maternal immunity declines approximately 6 months after birth on average [26]. A study on the antibody titer of children in Belgium [27] reported that (1) the maternal immunity of an infant born to a mother who had acquired immunity by vaccination was lower and also lost earlier than that of an infant born to a mother who had been infected with measles and (2) the loss of maternal immunity was not affected by the infant's weight, breast feeding, the educational level of the mother, or delivery by cesarean operation.…”

Real-time Investigation of Measles Epidemics with Estimate of Vaccine Efficacy

“…If the evaluation can be made based on readily available epidemiological datasets in real-time, disease control policy making will be able to reflect the results of such analysis. For instance, if we can detect the signature of a potential major epidemic in near future 7 or if we can identify specific sub-populations that are less protected than others 8, the epidemiological modeling study could improve real-time policy making, e.g. identifying an essential part of the population to be (re-)vaccinated.…”