A mixture model for the detection of Neosporosis without a gold standard

Neosporosis is a bovine disease caused by the parasite Neospora caninum. It is not yet sufficiently studied, and it is supposed to cause an important number of abortions. Its clinical symptoms do not yet allow the reliable identification of infected animals. Its study and treatment would improve if a test based on antibody counts were available. Knowing the distribution functions of observed counts of uninfected and infected cows would allow the determination of a cutoff value. These distributions cannot be estimated directly. This paper deals with the indirect estimation of these distributions based on a data set consisting of the antibody counts for some 200 pairs of cows and their calves. The desired distributions are estimated through a mixture model based on simple assumptions that describe the relationship between each cow and its calf. The model then allows the estimation of the cutoff value and of the error probabilities.