I am not a mathematician. I need to be able to frame my problem so I would like guidance on what type of problem this is and perhaps guidance on how to solve it.
I have patients with food allergies. I need to find what they are allergic to. I normally ask the patient to exclude all food types, perform a test to confirm their allergic response has gone and then reintroduce one food type at a time, testing at each reintroduction.
They are usually allergic to one of 6 possible food types. The probability of being allergic to each food type is as follows (we assume the probability of having one allergy is independent of the others)
fish 0.3 egg 0.2 soya 0.3 milk 0.6 wheat 0.4 rye 0.1
The idea of excluding all the foods and then reintroducing one at a time is probably a bit inefficient so I could follow an alternative structure such as remove one at a time and then retest, or remove two at a time, or remove all and then reintroduce two a time etc.
The problem I have is how do I determine the best reintroduction or exclusion path using which food types to determine which food type the patient is allergic to with the smallest number of steps.
Hopefully this is clear. I have a feeling someone may mention a Travelling Salesman type solution but is this correct and how would I incorporate probabilities into this? I am comfortable with R if a solution is provided in this format.