Motivated by this reference, it states under ROC Space
When evaluating a binary classifier, we often use a Confusion Matrix...however here we need only TPR and FPR
I'd feel more comfortable if the ROC were instead called positive-ROC suggesting there is an alternative ROC curve that is used from TNR and FNR. But that doesn't seem to be the case. Everywhere I've looked, ROC refers to using TPR and FPR, specifically.
Is there a version of the ROC curve that instead accounts to average the success of positive and negative example classification, say $\frac{1}{2}(ROC_{+} + ROC_-)$?, where $ROC_+$ is the popular metric using TPR/FPR and $ROC_-$ is the unpopular version of the same curve using TNR/FNR?
My question is, what makes TPR, FPR so much better than chosing TNR, FNR for the ROC curve? Why is it more important ( that is, ROC is a popular metric) to consider classification of positive examples than negative?