Decision Support Puzzles for Applied Mathematicians
February 2008 - Doctor Decision Tree
With flu season upon us, each of us has important decisions to make if and when we fall ill. In the interest of discussing decision trees, letís assume that youíve picked up an illness but youíre not sure if it is just a cold virus, a more severe flu virus, or a penicillin treatable bacterial infection.
There are two alternatives for you to consider:1.) Whether or not to see the doctor and have the doctor run the test to determine if the illness is a cold, flu, or bacterial.2.) Whether or not to treat the illness with penicillin (which will only be effective against a bacterial illness).
The cost to go to the doctor and have the test is $200 and the cost of a penicillin prescription is $50. The chance of the illness being a cold is 50%, flu is 20%, and bacterial is 30%. The test results also match these ratios. If the test indicates that it is a cold, then there is a 80% likelihood that it is a cold. If the test indicates a flu virus, then there is a 90% likelihood that it is the flu. If the test indicates that it is bacterial, then there is a 95% likelihood that it is a bacterial illness. The alternative outcomes are evenly divided among the likelihood balance. If the illness is a cold then you will miss 5 days of work which is a cost to you of $500.
If the illness is the flu then you will miss 8 days of work at a cost to you of $800. If the illness is bacterial and is not treated you will miss 12 days of work at a cost of $1200. If you correctly treat the bacterial illness you will only miss 2 days of work at a cost of $200.