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J R Soc Interface. 2010 Nov 6; 7(52): 1537–1544.
Published online 2010 Apr 14. doi: 10.1098/rsif.2010.0086
Michiel van Boven,1,* Mirjam Kretzschmar,1,2 Jacco Wallinga,1,2 Philip D O´Neill,3 Ole Wichmann,4 and Susan Hahné1
1Centre for Infectious Disease Control, National Institute for Public Health and the Environment, PO Box 1, 3720 Bilthoven, The Netherlands
2Julius Center for Health Research & Primary Care, University Medical Center Utrecht, PO Box 85500, 3508 Utrecht, The Netherlands
3School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
4Department for Infectious Disease Epidemiology, Robert Koch-Institute, DGZ-Ring 1, 13086 Berlin, Germany
*Author for correspondence (Email: ln.mvir@nevob.nav.leihcim).
Author information ▼ Article notes ► Copyright and License information ►
Received 2010 Feb 16; Accepted 2010 Mar 22.
Copyright © 2010 The Royal Society
This article has been cited by other articles in PMC.
Excerpts below; full text is at http://rsif.royalsocietypublishing.org/content/7/52/1537
We have obtained estimates of the reproduction number and vaccine efficacy of measles in a highly vaccinated public school. Our results confirm that measles virus is among the most transmissible of infectious diseases (Anderson & May 1991, p. 70), and suggest that it may even be more transmissible than hitherto thought. This indicates that even though estimated vaccine efficacy is high (0.997), this may not be enough to prevent major outbreaks unless the vaccination coverage is nearly 100 per cent. In fact, our results indicate that the vaccination coverage should be at least 0.971 (95% credible interval: 0.961–0.978). This high value is consistent with the experience of elimination in the Americas, where a high vaccination coverage augmented by catch-up campaigns was required for elimination, and it may help explain that outbreaks continue to occur in highly vaccinated populations in other parts of the World (Sutcliffe & Rea 1996; Paunio et al. 1998; Lynn et al. 2004; Yeung et al. 2005; Ong et al. 2007).
In our Bayesian analyses the unknown vaccination statuses are included as latent variables in a consistent framework. These analyses indicate that the 32 infected persons with unknown vaccination status are almost always unvaccinated (range: 31–32; median: 32), while the 338 uninfected persons with unknown vaccination status are mostly vaccinated (range: 332–338; median 338; table 2). These findings may seem surprising but can be understood if one realizes that if vaccine efficacy for susceptibility is high, it is far more probable that infected persons are unvaccinated than vaccinated, while the reverse is true for uninfected persons. Nevertheless, to investigate how the results are affected if some of the uninfected persons with unknown vaccination status are unvaccinated we have carried out analyses assuming that vaccination coverage in the uninfected persons with missing vaccination status corresponds to the observed vaccination coverage (782/(782 + 36) ≈ 0.96; figure 5). The analyses indicate that the basic reproduction number, vaccine efficacy, and critical vaccination coverage all decrease with increasing number of uninfected unvaccinated persons. Still, the estimated critical vaccination coverage remains higher than the vaccination coverage typically achieved in developed countries (0.958; 95% CI: 0.943–0.969).
More generally, in our main analyses (figures 22–4) imputation of the missing information is based on the likelihood contributions of the infectious contacts. One could take an alternative approach, based on the assumption that the probability that a person with missing vaccination status is vaccinated is determined by the observed vaccination coverage. For the specific case of the measles outbreak in Germany, however, it is difficult to reconcile the number of infections in the group with unknown vaccination status with the observed number of infections in the vaccinated and unvaccinated groups. To be specific, arguing along these lines one would expect out of 370 persons with unknown vaccination status to be unvaccinated. It is difficult to see how this figure can be matched with the observed number of infections in this group (32) and the infection attack rates in the unvaccinated and vaccinated groups (19/36 and 4/782).
Our definition of vaccine efficacy is based on an explicit epidemiological model, and has a clear-cut biological interpretation (reduction of the probability of infection per contact), making it possible to meaningfully average over populations and to extrapolate beyond the study population. This contrasts with traditional estimates of vaccine efficacy that are based on a comparison of attack rates in vaccinated and unvaccinated individuals, or by simply using the vaccination status of the infected individuals together with the population vaccination coverage (the screening method) (Orenstein et al. 1985). Vaccine efficacies estimated by these methods are lacking a clear biological interpretation, making it difficult to interpret the results and to extrapolate to different situations (Becker et al. 2003; Becker & Britton 2004; Halloran et al. 2010).
We have based our analyses on a single outbreak of measles in a single school, and one could argue that this limits the scope of our results. However, in recent years numerous measles outbreaks have been described in highly vaccinated populations (table 1), and we therefore believe that the critical vaccination coverage for measles virus may have been systematically underestimated. This could be due to the fact that estimates of measles reproduction numbers are often still based on serological studies from the pre-vaccination era. More recent analyses of outbreaks and long-term time series in the highly vaccinated populations of the Netherlands and the UK suggest that the fraction of the population that should be immune to prevent major outbreaks is approximately 96 per cent (Wallinga et al. 2003, 2005), and that the basic reproduction number is in the range 21–57 (Finkenstadt & Grenfell 2000; He et al. 2010; table 2).
Of course, we do not claim that measles basic reproduction numbers and vaccine efficacies are invariant, and do not differ between populations with differing contact intensities (e.g. households versus schools versus public space), vaccination composition and coverage, vital statistics (birth rates, life expectancy) and other demographic characteristics (e.g. age distribution, gender, socioeconomics). Still, we believe that it is of importance to analyse measles outbreaks of measles in high-contact settings such as households and schools because these may act as a multiplier of infection and driver of epidemics in heterogeneously vaccinated populations.
While we were able to obtain estimates of the efficacy of the vaccine in preventing infection in vaccinated persons, the design of the study makes it difficult to obtain estimates of the efficacy of the vaccine reducing the infectiousness of infected vaccinated persons (Basta et al. 2008). The reason is that with final size information from a single population it is difficult to disentangle the effect of the vaccine in reducing the probability of infection from the effect it may have in reducing infectiousness of infected vaccinated persons. To this end, other schools with different vaccination coverages and different attack rates in the vaccinated and unvaccinated subgroups should have been included. However, since the infection attack rates in vaccinated persons are very low in the German outbreak (Wichmann et al. 2009) the precision with which one can estimate the efficacy of the vaccine in reducing the infectiousness of infected vaccinated persons is likely to be poor.
Our finding that infected vaccinated individuals are to be expected despite the fact that vaccine efficacy is very high shows that the effectiveness of a vaccine in a population cannot be judged solely by its (estimated) efficacy, but also depends on the pathogen´s transmissibility. If vaccines are judged by their ability to induce herd immunity, then the requirements for what constitutes an adequate vaccine are much more stringent for a highly transmissible infectious disease such as measles than for other, less transmissible, infectious diseases. For instance, while for most infectious diseases a vaccine that is able to prevent transmission in more than 99.5 per cent of infectious contacts will certainly be able to prevent major outbreaks with current vaccination coverages, this is arguably not always the case for measles.
We would like to acknowledge the constructive comments of three anonymous reviewers which helped improve the manuscript.
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