Coordinates of the Curve
This table reports the sensitivity and 1-specificity for every possible cutoff for positive classification. The sensitivity is the proportion of HIV-positive samples with assay results greater than the cutoff. 1-specificity is the proportion of HIV-negative samples with assay results greater than the cutoff.
Cutoff 0 is equivalent to assuming that everyone is HIV-positive. Cutoff 9 is equivalent to assuming that everyone is HIV-negative. Both extremes are unsatisfactory, and the challenge is to select a cutoff that properly balances the needs of sensitivity and specificity.
For example, consider cutoff 5.5. Using this criterion, assay results of 6, 7, or 8 are classified as positive, which leads to a sensitivity of 0.978 and 1-specificity of 0.015. Thus, approximately 97.8% of all HIV-positive samples would be correctly identified as such, and 1.5% of all HIV-negative samples would be incorrectly identified as positive.
If 2.5 is used as the cutoff, 99.5% of all HIV-positive samples would be correctly identified as such, and 4.0% of all HIV-negative samples would be incorrectly identified as positive.
Your choice of cutoff is mandated by the need to closely match the sensitivity and specificity of traditional tests. The values in this table are at best guidelines for which cutoffs that you consider. This table does not contain error estimates. So there is no assurance of the accuracy of sensitivity or specificity for a cutoff in the table.
The final column in the table shows Youden’s index, which provides a numerical summary of the two types of accuracy at each possible cutoff point. As indicated in figure 2, the maximum value in this case is 0.971, corresponding to a cutoff value of 4.5. This measure treats false positive and false negative errors as equally important, so it is not useful in situations where one is markedly more important. The Gini index in figure 2 is a reexpression of the area under the ROC curve that results in a metric with a maximum value of 1, but where a 'chance classifier' scores 0 instead of 0.5, as is the case with the area under the ROC curve.
