Estimation of animal-level prevalence from pooled samples in animal production

Often, the prevalence of an infection in the animal-production sector is determined at the group level. The prevalence at animal level (p) gives more-precise information on the infection status of the sector. This paper shows that pooled-sample data together with mathematical models allow for estimation of p. For this, model assumptions have to be made on the variation of p between groups separated in space and/or time. Formulas were derived for four models that were based on different assumptions. Model 1 assumed that p has the same value for all groups. Models 2-4 assumed that some of the groups were not infected. In addition, model 2 assumed that p has the same value for all infected groups; model 3 assumed that for an infected group, p is equal to either p(1) or p(2); and model 4 assumed that p was Beta distributed among infected groups. The models were applied to data sets on Salmonella infection in broiler flocks, including serotype data dominated by S. Hadar and S. Paratyphi B, var. Java. Based on likelihood-ratio tests, models 3 and 4 consistently fitted significantly better to the data. The applicability of model 4 is numerically bounded, related to the shape of the Beta distribution of p. Model calculations show that flock-level prevalence of Salmonella is much higher after than before slaughter. This difference (which possibly is related to different types of samples) is much smaller at the animal level. An important result of the estimation of p is that it in turn allows for an estimation of the proportion of false-negative groups--which is important in estimating the effect of veterinary or public-health measures.