Assess sensitivity of a binary screening result across other continuous covariate(s)

I want to assess the sensitivity of a diagnostic screening test, which is a binary test (screen +ve and screen -ve). There is no continuous measure from this test - it is literally yes or no.

My question is, in addition to the sensitivity in the total sample, I would also like to see if there’s a difference in sensitivity across other continuous clinical factors, for eg, age - Does the test perform better in younger ages as opposed to older. Similarly, there are other continuous measures I would like to compare sensitivity across (less than 10 clinical factors).

One way, which I know throws out a lof of information, is binning the continuous predictor and assessing performance in each group. But how can I make use of the continuous data to assess a non-linear relationship between sensitivity and age?

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This is a good place for binary logistic regression as we used here, in which no binning is required. But note that since sensitivity and specificity vary they become useless as they only make probabilistic diagnosis more complex. More here in its Diagnosis chapter.

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