Evaluating the reliability of diagnostic performance indices by using Taguchi quality loss function

A medical test to diagnose a disease is often used to distinguish between healthy and diseased individuals, where early, accurate and reliable diagnosis can decrease morbidity and mortality rates of disease. An optimal cut-off point is required to discriminate healthy from diseased individuals, and a corresponding biomarker value is used to assess the accuracy and robustness whether a person is healthy (negative) or diseased (positive). If the biomarker values, that are greater than or equal to this cut-off value, are considered positive, otherwise they are negative. Several indices such as Youden index, Euclidean index, product of sensitivity and specificity have been used in clinical practices but their reliability of performance are not well understood by clinicians. This study uses Taguchi quality loss function to compare the choice of methods in determining optimal cut-off points for the diagnostic tests. The results illustrate that the variance of diseased populations is less than the variance of healthy populations and the loss coefficient of false negative results is greater than loss coefficient of the false positive results, the Youden index has a better performance; in other cases, the Euclidean index is a better measure. This paper proposes a Taguchi index based on the quality loss function can measure the diagnostic accuracy for differences in the sensitivity and specificity by minimizing the cost of false positive and false negative results. The proposed index can assess diagnostic tests and offer perfect discrimination.