Development of a method for Bayesian nonparametric ROC analysis with application to an ELISA for Johne's disease in dairy cattle

Six hundred and sixty-eight dairy cattle were tested for Johne's disease using a direct-fecal real-time polymerase chain reaction (rt-PCR), fecal culture, and serum enzyme-linked immunosorbent assay (ELISA). Likelihood ratios (LRs) were estimated for five categories of sample-to-positive (S/P) values for the ELISA: <0.1, 0.1-0.249, 0.25-0.399, 0.4-0.999, > or =1.0. The statistical method assumed a single multinomial model for cross-classified rt-PCR, fecal culture results, and ELISA category strata. Conditional dependence between tests was investigated by the inclusion of all possible pairwise dependence terms. Sensitivity covariance between ELISA and fecal culture was estimated as 0.017. Estimates for the accuracy of the ELISA at the usual cutoff of 0.25S/P was 67.2% and 95.2% for sensitivity and specificity, respectively for a model that adjusted for the dependence between ELISA and fecal culture. The area under the receiver-operating characteristic (ROC) curve (95% probability interval) for the ELISA was 0.867 (0.796, 0.928). Point estimates for likelihood ratios (95% probability intervals) were 0.24 (0.11, 0.38), 1.52 (0.48, 3.27), 2.49 (0.31, 13.4), 6.33 (2.54, 16.5), and 103 (25.0, 2412) for the categories <0.1, 0.1-0.249, 0.25-0.399, 0.4-0.999, >/=1.0, respectively. Assumptions concerning the underlying distribution of test results for infected and uninfected animals were not necessary and this model can be employed for the general estimation of LRs and ROC curves in absence of knowledge concerning true disease status.