Likelihood ratio estimation without a gold standard: a case study evaluating a brucellosis c-ELISA in cattle and water buffalo of Trinidad

The likelihood ratio (LR) is a measure of association that quantifies how many more times likely a particular test result is from an infected animal compared to one that is uninfected. They are ratios of conditional probabilities and cannot be interpreted at the individual animal level without information concerning pretest probabilities. Their usefulness is that they can be used to update the prior belief that the individual has the outcome of interest through a modification of Bayes' theorem. Bayesian analytic techniques can be used for the evaluation of diagnostic tests and estimation of LRs when information concerning a gold standard is not available. As an example, these techniques were applied to the estimation of LRs for a competitive ELISA (c-ELISA) for diagnosis of Brucella abortus infection in cattle and water buffalo in Trinidad. Sera from four herds of cattle (n=391) and four herds of water buffalo (n=381) in Trinidad were evaluated for Brucella-specific antibodies using a c-ELISA. On the basis of previous serologic (agglutination) test results in the same animals, iterative simulation modeling was used to classify animals as positive or negative for Brucella infection. LRs were calculated for six categories of the c-ELISA proportion inhibition (PI) results pooled for cattle and water buffalo and yielded the following estimations (95% probability intervals): <0.10 PI, 0.05 (0-0.13); 0.10-0.249 PI, 0.11 (0.04-0.20); 0.25-0.349 PI, 0.77 (0.23-1.63); 0.35-0.499 PI, 3.22 (1.39-6.84); 0.50-0.749 PI, 17.9 (6.39-77.4); > or =0.75 PI, 423 (129-infinity). LRs are important for calculation of post-test probabilities and maintaining the quantitative nature of diagnostic test results.