Performance of a test

i am trying to explain whether calculating the performance of a diagnostic test (Sens/spec) can be determined - if the reference 'gold' test for the disease is a composite containing the test in question.
eg. the test is serum rhubard >0.5. and the disease is confirmed if one of a/b/c/d ( and serum rhubarb >0.5 is one of those conditions)


Less is more. Stay pure. Stay poor.
I think you can get away with this. You can calculate the AUC for both and get the difference in values. A caveat may be that the gold-standard has a better SEN and SPEC than the screening and you would hope the gold standard did not have any FP or FN.
sorry i am mistaken. the disease is only confirmed only by using an invasive rarely done test. The 'one of a/b/c/d' is a selection of the available tests and having one of them makes the diagnosis only 'probable'.
Therefore where the test being studied is negative, the disease is only considered present as the result of another imperfect test.