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.

On the information hidden in a classifier distribution.

Classification tasks are a common challenge to every field of science. To correctly interpret the results provided by a classifier, we need to know the performance indices of the classifier including its sensitivity, specificity, the most appropriate cut-off value (for continuous classifiers), etc. Typically, several studies should be conducted to find all these indices. Herein, we show that they already exist, hidden in the distribution of the variable used to classify, and can readily be harvested. An educated guess about the distribution of the variable used to classify in each class would help us to decompose the frequency distribution of the variable in population into its components-the probability density function of the variable in each class. Based on the harvested parameters, we can then calculate the performance indices of the classifier. As a case study, we applied the technique to the relative frequency distribution of prostate-specific antigen, a biomarker commonly used in medicine for the diagnosis of prostate cancer. We used nonlinear curve fitting to decompose the variable relative frequency distribution into the probability density functions of the non-diseased and diseased people. The functions were then used to determine the performance indices of the classifier. Sensitivity, specificity, the most appropriate cut-off value, and likelihood ratios were calculated. The reference range of the biomarker and the prevalence of prostate cancer for various age groups were also calculated. The indices obtained were in good agreement with the values reported in previous studies. All these were done without being aware of the real health status of the individuals studied. The method is even applicable for conditions with no definite definitions (e.g., hypertension). We believe the method has a wide range of applications in many scientific fields.