Relations among sensitivity, specificity and predictive values of medical tests based on biomarkers

Diagnostic tests are usually based on some quantitative biomarkers. Two key parameters used to characterise the quality of a test are test sensitivity and specificity. Predictive values of the disease status based on test results are also of interest in medical research and public health management. In this paper, we study the relations among sensitivity, specificity and predictive values of the test. The core concept is risk function, which is assumed to be an increasing function of the biomarker. Our results show that test sensitivity and specificity change in opposite directions. The positive predictive value and the sensitivity also change in opposite directions. Likewise, the negative predictive value and the specificity change in opposite directions.