Statistical Tests for Proportion Difference in One-to-Two Matched Binary Diagnostic Data: Application to Environmental Testing of Salmonella in the United States

Pooled sample testing is an effective strategy to reduce the cost of disease surveillance in human and animal medicine. Testing pooled samples commonly produces matched observations with dichotomous responses in medical and epidemiological research. Although standard approaches exist for one-to-one paired binary data analyses, there is not much work on one-to-two or one-to-N matched binary data in the current statistical literature. The existing Miettinen’s test assumes that the multiple observations from the same matched set are mutually independent. In this paper, we propose exact and asymptotic tests for one-to-two matched binary data. Our methods are markedly different from the previous studies in that we do not rely on the mutual independence assumption. The emphasis on the interdependence of observations within a matched set is inherent and attractive in both human health and veterinary medicine. It can be applied to all kinds of diagnostic studies with a one-to-two matched data structure. Our methods can be generalized to the one-to-N matched case. We discuss applications of the proposed methods to the environmental testing of salmonella in the United States.