Diagnostic Availability (DA) based on Pythagorean Theorem as a Novel Index for Integrative Evaluation of Diagnostic Tests

Accurate diagnosis is the prerequisite for effective treatment of diseases. Various biostatistics indices have been used to evaluate the performance of diagnostic tests. The distribution of test results commonly shows a relatively fixed overlap between the diseased and non-diseased populations, and the two main properties of laboratory tests sensitivity (Se) and specificity (Sp) usually demonstrate an inverse relationship of each other. An inverse relationship is also seen in the two sides of a right triangle where the hypotenuse serves as an integrated functional index of the two sides, as reflected in the geometric equation Pythagorean Theorem (PT). We have developed a novel test performance index named diagnostic availability (DA) based on the theory of PT, which integrates and reflects the combined efficiency of Se and Sp. When Se and Sp were changing inversely as seen in the vast majority of clinical settings, DA was superior to the other indices diagnostic efficiency (DE), Youden index, and Kappa coefficient (К) in reflecting the overall test performance of a test. It was also the only one responsive to the reciprocal changes of Se and Sp. Therefore, we propose the additional consideration of DA besides Se and Sp during the determination of the optimal test result cut-off point. In the rare scenarios that Se and Sp are changing in the same direction, DA, J and К outperforms DE in reflecting test performance. Furthermore, DA can also help identify the better test when two tests exhibit similar areas under the curve (AUC) in the receiver operating characteristic curve (ROC) analysis. In conclusion, DA is a novel index for overall performance evaluation of diagnostic tests reflecting the combined efficiency of Se and Sp. It shows superiority over other commonly used indices in the assessment of overall test performance and serves as a valuable addition to the existing indices.