Bayesian mixture models for partially verified data: age- and stage-specific discriminatory power of an antibody ELISA for paratuberculosis.

Bayesian mixture models can be used to discriminate between the distributions of continuous test responses for different infection stages. These models are particularly useful in case of chronic infections with a long latent period, like Mycobacterium avium subsp. paratuberculosis (MAP) infection, where a perfect reference test does not exist. However, their discriminatory ability diminishes with increasing overlap of the distributions and with increasing number of latent infection stages to be discriminated. We provide a method that uses partially verified data, with known infection status for some individuals, in order to minimize this loss in the discriminatory power. The distribution of the continuous antibody response against MAP has been obtained for healthy, MAP-infected and MAP-infectious cows of different age groups. The overall power of the milk-ELISA to discriminate between healthy and MAP-infected cows was extremely poor but was high between healthy and MAP-infectious. The discriminatory ability increased with increasing age. The great overlap between the distributions of the different infection stages would have hampered our ability to discriminate between the different infection stages. Thus, the proposed method, which uses partially verified data on the true status for some individuals, is an intuitive extension to the standard non-gold standard methods, especially in the case of infections with a long latent period.