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!


Less is more. Stay pure. Stay poor.
Do you have a gold standard or basing this on other empiric results?

Passes test means negative results for liver cancer?


Less is more. Stay pure. Stay poor.
You might be interested in reading pages 55-56 in Clinical Epidemiology: The essentials, by RH Fletcher and SW Fletcher.