Calculation of lower bounds on the sensitivity and specificity of diagnostic tests: relevance to the diagnosis of noise-induced hearing loss

Objective: To derive lower bounds for the sensitivity and specificity of diagnostic tests when there is no gold standard method of diagnosis and to illustrate how the results can be applied to tests for diagnosing noise-induced hearing loss (NIHL). Design: It is demonstrated mathematically that provided a test has some diagnostic value (proportion of hits greater than proportion of false alarms), the sensitivity of the test must be greater than the proportion of individuals who receive a positive diagnosis using that test and the specificity must be greater than 1 minus the proportion of individuals who receive a positive diagnosis. The sensitivity and specificity of tests for diagnosing NHIL are best evaluated using populations with high and low likelihoods of having NIHL, respectively. Results: The derivations are illustrated using two tests for the diagnosis of military NIHL based on the audiogram and age. A test based on a multi-layer perceptron had a sensitivity probably above 0.986 and a specificity probably above 0.902, with lower bounds of 0.965 and 0.848, respectively, after allowing for sampling errors. Conclusions: Although the lack of a gold standard prevents precise estimation of sensitivity and specificity, lower bounds can be placed on their values.