An alternative to Youden's index of diagnostic accuracy

Although Youden's index J has been a widely used summary measure of medical diagnostic accuracy, it suffers from a paradoxical property: the value of J can be very small even if the observed proportional accuracy (proportion of correct test results) is near perfect. The J paradox is defined and discussed, explaining the need for an alternative index. Exploratory analysis of alternative index formulations produced one particular index that overcomes the J paradox and has all the desirable properties expected of a diagnostic accuracy index. An important basis for such an index was the requirement that the index should account for the fact that some component of the diagnostic accuracy could be due to chance results. The analysis was based on analytical and statistical reasoning as well as empirical data, including real medical diagnostic data from various reported studies. The new diagnostic accuracy index A resulting from the analysis is found to have desirable properties, avoids the J paradox, and takes on values that are entirely reasonable. The outlined statistical inference procedure can be used to construct approximate confidence intervals. The index A is also generalized to a weighted equivalent \({A}_{w}\) for which different weights or emphasis can be placed on false negative test results and false positive results. The indices A and \({A}_{w}\) can also be easily extended to potential situations involving multiple diagnostic categories. The new index A (and its weighted form \({A}_{w}\) ) is proposed as a preferred alternative to Youden's J . While J can in some realistic real situations produce results that would seem to be entirely unreasonable, unjustifiable, and misleading, A (and \({A}_{w}\) ) appears to take on values that all all realistic and plausible.