Estimating vaccination coverage for the trivalent measles–mumps–rubella vaccine from trivariate serological data

Abstract

The effectiveness of childhood immunization programs depends on the vaccination coverage actually achieved. Routinely collected coverage data are not always available, and comparability between countries is often compromised because of different data collection methods. In 2000, Gay developed a method to estimate trivalent vaccination coverage from readily available trivariate serological data on the basis of parametric assumptions related to the rate of seroconversion for each vaccine component and probabilities of natural exposure to infection. Gay's work was indirectly published in a paper by Altmann and Altmann, who derived exact solutions for the parameters on the basis of Gay's modeling equations. In this paper, we propose a general likelihood-based marginal model framework to extend Gay's model by relaxing two of its main assumptions. We use the Bahadur model for trivariate binary data to explicitly account for an association between the disease-specific exposure probabilities. We fit several correlation structures to measles, mumps, and rubella serology from Belgium and Ireland. For both countries, we estimate a small positive pairwise exposure correlation, which improves the fit to the data. However, the effect on the estimated vaccination coverage and its associated variability is fairly moderate. For both Belgium and Ireland, all models reveal that the vaccination coverage achieved during the first 15 years since the introduction of measles, mumps, and rubella immunization is insufficient to eliminate measles.

Estimating the immunogenicity of measles-rubella vaccination administered during a mass campaign in Lao People’s Democratic Republic using multi-valent seroprevalence data

“…Following the approach of Gay 16 (unpublished) (described in Altmann and Altmann 17 ) and Goeyvaerts et al . 6 , it can be shown (Supporting Material) that p a,m,r can be expressed in terms of the following factors:The vaccination coverage ( v a ) in age group a during the SIA in 2011, assumed to be identical for all age groups..The proportion of people in age group a who were not vaccinated during the SIA in 2011 who acquired antibodies to infection i (denoted c am and c ar for measles and rubella respectively), assumed to differ between each single year age band. For measles, these people would have become seropositive because of natural infection or vaccination; for rubella, they would have become seropositive because of natural infection.The proportion of people who were negative for antibodies to infection i just before the SIA in 2011, but then became positive for antibodies to infection i because of vaccination, assumed to be identical for all ages (denoted e m and e r for measles and rubella respectively).…”

“…Such analyses also allow estimation of the vaccination coverage, allowing verification of reported levels of coverage. To our knowledge, the only studies to date which have estimated the immunogenicity using such analyses considered the measles-mumps-rubella (MMR) vaccine in Western countries and found levels of seroconversion of at least 94% for the measles and rubella components 6,7 , even when adjusting for possible waning in seroprevalence following vaccination 7 .…”

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

“…The variability in values for the E and I durations in Table suggests limited agreement about the durations for average exposure and infection periods. The review process also revealed many excluded studies that estimated model inputs, which similarly showed a wide range of assumptions. Hypothetical modeling showed the importance of including the latency period and explored different formulations for seasonality in measles and rubella models .…”