I have come across the following optimization problem:
"A patient presents himself with symptoms to a physician. The physician has a set of $n$ medical tests, where each test $i$ has costs $c_i$ associated with it and returns a perfectly reliable result (usually positive/negative). The physician can perform these medical tests to decide which medication to prescribe. The physician knows rules like
- If test A is positive and test B is negative, prescribe medication X.
- If test C is positive, also prescribe X.
- In all other cases prescribe Y.
Given these rules and the costs of all the tests, which sequence of medical tests should the physician choose in order to minimize the expected treatment cost?"
Unfortunately, I have a hard time finding any information about this problem. Is there a specific name I can google for? Or alternatively, can someone point me to a mathematically rigorous formulation?
Basically, I would like to do a literature review on this problem, but with all the economic debates about medical costs and insurances its pretty hard to find anything on the Web.