Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

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On the estimation of epidemiological parameters from serological survey data using Bayesian mixture modelling
Emanuele Del Fava, Piero Manfredi, Ziv Shkedy

Last modified: 2018-05-31


In the context of serological surveys for the estimation of important epidemiological functions, mixture models offer an alternative and more accurate approach than the conventional one based on the diagnostic assay’s cut-off points. In this work, we propose an innovative Bayesian mixture model for the estimation of flexible models for the age-specific seroprevalence and force of infection (or incidence rate). In order to account for the possible waning of immunity by age, we propose a Bayesian variable selection approach to determine the best age-specific model for the mean and the variance of the seropositive subpopulation. Our methodology is applied to a sample of antibody titres to varicella from Italy. Our results confirm that mixture models are a flexible and highly customisable tool, adapt to be systematically used in serological surveys.


  1. Azzalini, A.: A Class of Distributions Which Includes the Normal Ones. Scand. J. Statist. 12, 171—178 (1985) doi:10.2307/4615982.
  2. Bollaerts, K., Aerts, M., Shkedy, Z., Faes, C., Van der Stede, Y., Beutels, Ph., Hens, N.: Estimating the Population Prevalence and Force of Infection Directly From Antibody Titres. Statist. Mod. 12, 441—462 (2012) doi:10.1177/1471082X12457495.
  3. Del Fava, E., Mirinaviciute, G., Flem, E., Freiesleben de Blasio, B., Scalia Tomba, G., Manfredi, P.: Estimating Age-Specific Immunity and Force of Infection of Varicella Zoster Virus in Norway Using Mixture Models. PLoS ONE 11, e0163636—12 (2016) doi:10.1371/journal.pone.0163636.
  4. Del Fava, E., Shkedy, Z., Bechini, A., Bonanni, P., Manfredi, P.: Towards Measles Elimination in Italy: Monitoring Herd Immunity by Bayesian Mixture Modelling of Serological Data. Epidemics 4, 124—31 (2012) doi:10.1016/j.epidem.2012.05.001.
  5. Diebolt, J., Robert, C.P.: Estimation of Finite Mixture Distributions Through Bayesian Sampling. J. R. Statist. Soc. B 56, 363—75 (1994)
  6. Evans, R.B., Erlandson, K.: Robust Bayesian Prediction of Subject Disease Status and Population Prevalence Using Several Similar Diagnostic Tests. Statist. Med. 23, 2227—2236 (2004) doi:10.1002/sim.1792.
  7. Frühwirth-Schnatter, S., Pyne, S.: Bayesian Inference for Finite Mixtures of Univariate and Multivariate Skew-Normal and Skew-T Distributions. Biostatistics 11, 317—336 (2010) doi:10.1093/biostatistics/kxp062.
  8. Gabutti, G., Rota, M.C., Guido, M., De Donno, A., Bella, A., Ciofi degli Atti, M.L., Crovari, P.: The Epidemiology of Varicella Zoster Virus Infection in Italy. BMC Pub. Health 8, 372 (2008) doi:10.1186/1471-2458-8-372.
  9. George, E., McCulloch, R.E.: Variable Selection via Gibbs Sampling. J. Am. Statist. Assoc. 88, 881—889 (1993)
  10. Hardelid, P., Williams, D., Dezateux, C., Tookey, P.A., Peckham, C.S., Cubitt, W.D., Cortina-Borja, M.: Analysis of Rubella Antibody Distribution From Newborn Dried Blood Spots Using Finite Mixture Models. Epidemiol. Infect. 136, 1698 (2008) doi:10.1017/S0950268808000393.
  11. Kasim, A., Shkedy, Z., Kato, B.S.: Estimation and Inference Under Simple Order Restrictions: Hierarchical Bayesian Approach. In: Dan L., Shkedy, Z., Yekutieli, D., Amaratunga, D., Bijnens (eds.) Modeling Dose-Response Microarray Data in Early Drug Development Experiments Using R. Springer, Heidelberg.
  12. Metcalf, C.J.E., Farrar, J., Cutts, F.T., Basta, N.E., Graham, A.L, Lessler, J.T.,  Ferguson, N.M., Burke, D.S., Grenfell, B.T.: Use of Serological Surveys to Generate Key Insights Into the Changing Global Landscape of Infectious Disease. Lancet 388, 728–730 (2016) doi:10.1016/S0140-6736(16)30164—7.
  13. O'Hara, R.B., Sillanpää, M.J.: A Review of Bayesian Variable Selection Methods: What, How and Which. Bayes. Anal. 4, 85—117 (2009) doi:10.1214/09-BA403.
  14. Rota, M.C., Massari, M., Gabutti, G., Guido, M., De Donno, A., Ciofi degli Atti, M.L.: Measles Serological Survey in the Italian Population: Interpretation of Results Using Mixture Model. Vaccine 26, 4403—4409 (2008) doi:10.1016/j.vaccine.2008.05.094.
  15. Vyse, A.J., Gay, N.J., Hesketh, L.M., Morgan-Capner, P., Miller, E.: Seroprevalence of antibody to varicella zoster virus in England and Wales in children and young adults. Epidemiol. Infect. 132, 1129-1134 (2004)

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