Calculating Sensitivity and Specificity of Combined Testing...With a Surprise.

Ok guys. I have an interesting question.

I'm a biomedical engineering student from Georgia Tech and for one of my classes I have to implement screening policy for liver cancer. I decided to implement combined testing. It looks like this

Test A
High risk factor - - Test C
Test B

I have a series of tests, and the first tests are in parallel. If the patient passes test A or B, they move on to Test C. I can calculate the sensitivity and specificity of this system, given the sensitivities and specificity of each test, that's no problem. My problem comes after Test C.

If Test C comes out negative, I have the patient do the screening process again. In which case if he passes the parallel tests and then fails Test C again I consider him negative, so it loops only once. How can I take this into account?

I'm looking at sensitivities and specificity, so I think the prevalence of the disease don't matter. I'm assuming, of course, that each test has the same sensitivity and specificity a second time.

Help would be greatly appreciated!


Not a robit
You might be interested in reading pages 55-56 in Clinical Epidemiology: The essentials, by RH Fletcher and SW Fletcher.