Estimating vaccination coverage for the trivalent MMR vaccine from trivariate serological data

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.