ROC curve

[Jatinjain]

Why ROC curve is created between sensitivity and 1-specificity? Why it is 1 minus? Why it can't be 1- sensitivity?

[Rick_SAS]

There is a tradeoff between sensitivity and specificity. 

Sensitivity = 1 - Probability(Type II error)

Specificity = 1 - Probability(Type I error)

Therefore 1 - Specificity  = Probability(Type I error).

It would be fine to graph either Specificity or 1-Specificity (and the same for Sensitivity). The graph would contain the same information. The ROC curve makes one choice and is a standard way to look at the tradeoff.

[Jatinjain]

I am sorry but still I am not able to understand. Can you please support the explanation with some kind of plot?

[StatDave]

As you increase the cutpoint on the predicted probabilities from 0 to 1, the sensitivity decreases and the specificity increases. See the Classification Table (resulting from the CTABLE option) shown at the end of the example titled "Stepwise Logistic Regression and Predicted Values" in the LOGISTIC documentation. By plotting sensitivity against 1-specificity, the point at which sensitivity is zero can be placed at the lower left corner of the plot since 1-specificity is also zero. Similarly, when sensitivity=1, 1-specificity is also 1 so that point can appear in the upper right corner of the plot.