The choice of methods in determining the optimal cut-off value for quantitative diagnostic test evaluation

Introduction The choice of criteria in determining optimal cut-off value is a matter of concern in quantitative diagnostic tests. Several indexes such as Youden's index, Euclidean index, product of sensitivity and specificity in receiver operator characteristic space and diagnostic odds ratio have been used in clinical practices but their advantages and limitations are not well understood by clinicians. This study aimed to compare these methods in determining optimal cut-off values for quantitative diagnostic test. Methods The different configurations of binormal and bilogistic distributions with equal and unequal variances for nondiseased and diseased subjects were examined. The cut-off values with increment of 0.1 in Z-scale were varied. Then, the Youden's index, Euclidean index, product of sensitivity and specificity, and diagnostic odds ratio were calculated over various cut-off values under distributional assumptions with confirmed parameters. Results According to the obtained data from binormal model and equal variances, the optimal cut-off values derived from Youden's index, Euclidean index, and product method were similar but the diagnostic odds ratio yielded either extremely low or extremely high optimal cut-off value. For bilogistic pair distributions with equal variances, the Youden's, Euclidean indexes and product method resulted in an identical cut-off value but the diagnostic odds ratio was constant over various cut-points. By both binormal and bilogistic data with more variations in nondiseased population, the Youden's index produced a higher sensitive optimal cut-off value; but with more variation for diseased distribution, the Euclidean index showed a more sensitive optimal cut-off. For bilogistic data with unequal variance, the log(diagnostic odds ratio) had a straight line relationship over cut-off values with either positive or negative slope. Conclusion As a measure of association, diagnostic odds ratio cannot be informative in determining an optimal cut-off value. The advantage of receiver operator characteristic analysis to obtain the optimal cut-off value is to use Youden's index, Euclidean index, or product index which is recommended. The choice between them depends on variability of test results in diseased and nondiseased subjects and the desired sensitivity.