Log-linear and logistic modeling of dependence among diagnostic tests

We developed log-linear and logistic-modeling approaches to investigate dependence among diagnostic tests. To illustrate the approaches, we used published data for swine toxoplasmosis, bovine paratuberculosis, and swine brucellosis. These diseases were selected because each animal's true disease status was known, at least five tests were used, and the serologic tests had been previously shown to have moderate-to-high pairwise dependence in test sensitivities (and sometimes in test specificities). Log-linear and logistic modeling yielded similar results for swine toxoplasmosis and swine brucellosis. However, logistic modeling could not be used to investigate test dependence for bovine paratuberculosis because of quasi-separation in the data attributable to two fecal-based tests having specificities of 100%. Findings from our modeling indicated that 3 (modified agglutination, enzyme-linked immunosorbent assay (ELISA), latex agglutination) of 5 serologic tests for toxoplasmosis and 2 (rivanol and particle concentration fluorescence immunoassay) of 6 serologic tests for brucellosis were adequate for diagnosis. For bovine paratuberculosis, both fecal-based tests (Herrold's egg-yolk culture and radiometric culture) and 1 (ELISA) of 3 serologic tests were necessary in serial and parallel testing schemes.