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PLoS One. 2016 Aug 18;11(8):e0161109. doi: 10.1371/journal.pone.0161109. eCollection 2016.

A Bivariate Mixture Model for Natural Antibody Levels to Human Papillomavirus Types 16 and 18: Baseline Estimates for Monitoring the Herd Effects of Immunization.

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Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, the Netherlands.
Department of Epidemiology and Biostatistics, VU University Medical Centre, Amsterdam, the Netherlands.
Department of Statistics, Informatics and Modelling, National Institute for Public Health and the Environment, Bilthoven, the Netherlands.


Post-vaccine monitoring programs for human papillomavirus (HPV) have been introduced in many countries, but HPV serology is still an underutilized tool, partly owing to the weak antibody response to HPV infection. Changes in antibody levels among non-vaccinated individuals could be employed to monitor herd effects of immunization against HPV vaccine types 16 and 18, but inference requires an appropriate statistical model. The authors developed a four-component bivariate mixture model for jointly estimating vaccine-type seroprevalence from correlated antibody responses against HPV16 and -18 infections. This model takes account of the correlation between HPV16 and -18 antibody concentrations within subjects, caused e.g. by heterogeneity in exposure level and immune response. The model was fitted to HPV16 and -18 antibody concentrations as measured by a multiplex immunoassay in a large serological survey (3,875 females) carried out in the Netherlands in 2006/2007, before the introduction of mass immunization. Parameters were estimated by Bayesian analysis. We used the deviance information criterion for model selection; performance of the preferred model was assessed through simulation. Our analysis uncovered elevated antibody concentrations in doubly as compared to singly seropositive individuals, and a strong clustering of HPV16 and -18 seropositivity, particularly around the age of sexual debut. The bivariate model resulted in a more reliable classification of singly and doubly seropositive individuals than achieved by a combination of two univariate models, and suggested a higher pre-vaccine HPV16 seroprevalence than previously estimated. The bivariate mixture model provides valuable baseline estimates of vaccine-type seroprevalence and may prove useful in seroepidemiologic assessment of the herd effects of HPV vaccination.

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