Inferences for likelihood ratios in the absence of a "gold standard"

Likelihood ratios are extensively used to evaluate the performances of diagnostic tests and to update prior odds of disease to posttest odds. Since few tests are truly 100% accurate, including many used as "gold standards," it is important to be able to estimate likelihood ratios in cases where no such standard is available. In this paper, methods to calculate point and interval estimates for likelihood ratios are described. The results numerically coincide with those reviewed by Centor when a "gold standard" is assumed available, but typically provide wider interval estimates when such a standard is not available, reflecting the increased uncertainty inherent in such situations. Unlike previous techniques, the methods do not require normal approximations or logarithmic transformations, and hence provide accurate estimates even when parameter distributions are highly skewed. The methods are illustrated using the results of two different diagnostic tests for the presence of an intestinal parasitic infection.