Estimating the burden of pertussis in Mexican adolescents from paired serological data by using a bivariate mixture model

type="main" xml:id="rssc12051-abs-0001"> <title type="main">Summary</title> <p>In recent decades there has been an increase in the reported incidence of clinical pertussis in many countries. Estimation of the true circulation of the bacterium Bordetella pertussis is most reliably made on the basis of studies that measure antibody concentrations against pertussis toxin. Antibody levels decay over time and provide a fading memory of the infection. We develop a discrete bivariate mixture model for paired antibody levels in a cohort of 1002 Mexican adolescents who were followed over the 2008–2009 school year. This model postulates three groups of children based on past pertussis infection; never, prior and new. On the basis of this model we directly estimate incidence and prevalence, and select a diagnostic cut-off for classifying children as recently infected. We also discuss a relatively simple approach that uses only ‘discordant’ children who test positively on one visit and negatively on the other. The discordant approach provides inferences that are very similar to those of the full model when the data follow the assumed full model. Additionally, the discordant method is much more robust to model misspecification than the full model which has substantial problems with optimization. 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% sensitvity.