I have 2-classes labelled data on which I'm performing classification using multiple classifiers. And the datasets are well balanced. When assessing the classifiers' performance, I need to take into consideration how accurate the classifier is in determining not only the true positives, but the true negatives also. Therefore, if I use accuracy, and if the classifier is biased toward positives and classifies everything as positive, I will get around 50% accuracy, even though it failed at classifying any true negatives. This property is extended to precision and recall as they focus on one class only, and in turn to F1-score. (This is what I understand even from this paper for example "[Beyond Accuracy, F-score and ROC: a Family of Discriminant Measures for Performance Evaluation](http://aaaipress.org/Papers/Workshops/2006/WS-06-06/WS06-06-006.pdf)").

Therefore, I can use sensitivity and specificity (TPR and TNR) to see how the classifier performed for each class, where I aim to maximize these values.

My question is that **I am looking for a measure that combines both these values into one meaningful measure**. I looked into the measures provided in that paper, but I found it to be non-trivial. And based on my understanding I was wondering why can't we apply something like the F-score, but instead of using precision and recall I would use sensitivity and specificity? So the formula would be
$$
\text{my Performance Measure} = \frac{2 \* \text{sensitivity} \* \text{specificity}}{\text{sensitivity} + \text{specificity}}
$$
and my aim would be to maximize this measure. I find it to be very representative. Is there a similar formula already? And would this make sense or is it even mathematically sound?