No need for a gold-standard test: on the mining of diagnostic test performance indices merely based on the distribution of the test value

BACKGROUND: Diagnostic tests are important in clinical medicine. To determine the test performance indices — test sensitivity, specificity, likelihood ratio, predictive values, etc. — the test results should be compared against a gold-standard test. Herein, a technique is presented through which the aforementioned indices can be computed merely based on the shape of the probability distribution of the test results, presuming an educated guess. METHODS: We present the application of the technique to the probability distribution of hepatitis B surface antigen measured in a group of people in Shiraz, southern Iran. We assumed that the distribution had two latent subpopulations — one for those without the disease, and another for those with the disease. We used a nonlinear curve fitting technique to figure out the parameters of these two latent populations based on which we calculated the performance indices. RESULTS: The model could explain > 99% of the variance observed. The results were in good agreement with those obtained from other studies. CONCLUSION: We concluded that if we have an appropriate educated guess about the distributions of test results in the population with and without the disease, we may harvest the test performance indices merely based on the probability distribution of the test value without need for a gold standard. The method is particularly suitable for conditions where there is no gold standard or the gold standard is not readily available. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-023-01841-8.