Which one is the best to choose…
A test with high specificity and low sensitivity.
Or, a test with a high sensitivity and low specificity?
And why?
There is a tradeoff between the sensitivity and the specificity, the higher one of them, the lower the other.
Therefore the choice defends on what’s important to you:
If it is more important to have a higher probability of positive diagnosis given the patient is positive then you should lean to higher sensitivity. On the other hand, if it is more important to have a higher probability of negative diagnosis given the patient is negative then you should lean toward higher specificity.
That leaves us wanting to know if sensitivity and specificity are useful. I think not. They condition on the unknown to compute probabilities of the already known quantities (test results). Once you have a diagnostic probability model everything is direct, and developing such a model can avoid sens and spec unless doing a case-control study. More at fharrell.com/post/backwards-probs
You meant to say? If it is important to have high probability of positive test given patient has disease(which is unknown at the time test is ordered), then you should lean to higher sensitivity… And the same for specificity…