I have an empirical estimate of a ROC curve, that is, a plot of the sensitivity versus 1-specificity over all possible cut-off values of the marker. Based on an empirical ROC curve, I would like to determine the optimal cut-off point that represents a better trade-off between sensitivity and specificity. I have read that the Youden Index can be used in that purpose.
Here is an example:
oneMinusSpecificity <- c(1.00000000, 0.636363636, 0.436363636, 0.315151515, 0.163636364, 0.096969697, 0.072727273, 0.006060606, 0.000000000) sensitivity <- c(1.00000000, 0.91566265, 0.77108434, 0.66265060, 0.39759036, 0.33734940, 0.28915663, 0.07228916, 0.00000000)
which results in the following ROC curve. The vertical line represents the Youden index = largest distance between "1 - specificity" and "sensitivity".
> youden <- max(sensitivity - oneMinusSpecificity) > youden  0.3474991
How can I calculate the optimal cut-off using this information?