Faculty/Staff Daily Digest

Despite high childhood vaccination coverage, in recent decades there has been an increase in the reported incidence of clinical pertussis in many countries, especially among adolescents and adults. Estimation of the true circulation of the bacterium  Bordetella pertussis are most reliably made based on prospective studies in defined populations that measure antibody concentrations against pertussis toxin.  Such antibodies are proteins produced by the adaptive immune system to fight {\it B. pertussis} exposure.  Antibodies decay over time and thus provide a fading memory of the infection. To estimate pertussis exposure, most studies have derived diagnostic cut-off points for pertussis antibody levels based on a single readout for each person.

In this paper we develop a discrete bivariate mixture model for paired antibody levels in a cohort of 1002 Mexican adolescents who were followed over the 2008-20009 school year. This model postulates three groups of children according to their pertussis infection status; children who have never been infected, infected before the start of the study and infected during follow-up. Based on this model we can directly estimate incidence, prevalence, and a diagnostic cut-off for classifying children as recently infected. We also discuss a relatively simple approach using only “discordant” children who are positive on one visit and negative on the other.  We show how the simple approach provides inferences very similar to the full but is much more robust and has better mean squared error under model mis-specification.

We additionally demonstrate how paired data can be enormously more efficient than cross-sectional data in estimating key parameters.

Using either the bivariate mixture or simple approach, we estimate the school year incidence of pertussis to be about 3% and the prevalence to be about 8%.  A cut-off of 50 was estimated to have about 99.5\% specificity and 68\% specificity.