Bayesian mixture models for within-herd prevalence estimates of bovine paratuberculosis based on a continuous ELISA response.

Diagnostic inference by use of assays such as ELISA is usually done by dichotomizing the optical density (OD)-values based on a predetermined cut-off. For paratuberculosis, a slowly developing infection in cattle and other ruminants, it is known that laboratory factors as well as animal specific covariates influence the OD-value, but while laboratory factors are adjusted for, the animal specific covariates are seldom utilized when establishing cut-offs. Furthermore, when dichotomizing an OD-value, information is lost. Considering the poor diagnostic performance of ELISAs for diagnosis of paratuberculosis, a framework for utilizing the continuous OD-values as well as known coavariates could be useful in addition to the traditional approaches, e.g. for estimating within-herd prevalences. The objective of this study was to develop a Bayesian mixture model with two components describing the continuous OD response of infected and non-infected cows, while adjusting for known covariates. Based on this model, four different within-herd prevalence indicators were considered: the mean prevalence in the herd; the age adjusted prevalence of the herd for better between-herd comparisons; the rank of the age adjusted prevalence to better compare across time; and a threshold-based prevalence to describe differences between herds. For comparison, the within-herd prevalence and associated rank using a traditional dichotomization approach based on a single cut-off for an OD corrected for laboratory variation was estimated in a Bayesian model with priors for sensitivity and specificity. The models were applied to the OD-values of a milk ELISA using samples from all lactating cows in 100 Danish dairy herds in three sampling rounds 13 months apart. The results of the comparison showed that including covariates in the mixture model reduced the uncertainty of the prevalence estimates compared to the cut-off based estimates. This allowed a more informative ranking of the herds where low ranking and high ranking herds were easier to identify.