To understand what decision analysis is, it is useful to consider a simple example for the management of sore throat. The model begins with a “decision node” that represents the decision to either order a test and treat based on the test results, or to simply treat all patients empirically with antibiotics:
Of course, some patients will have strep (and benefit from antibiotics) while others don’t have strep (and do not benefit, or even suffer a reduction in quality of life due to adverse drug effects and inconvenience):
However, tests aren’t perfect. The decision tree therefore has to take into account the fact that there are false positives and false negatives as well as true negative and true positive results:
In a decision analysis, probabilities are assigned to each “chance node” based on the medical literature. In the above example there are a number of chance nodes. The first two are determined by the probability of strep in the population, which is about 20% (or 0.2 in probability notation). The next two are determined by the accuracy of the rapid antigen test. A test that is 90% sensitive will give a positive result for 90% of patients with strep, and if it is 90% specific it will give a negative result for 90% of those without strep. The probability of an event occurring, and a branch being followed, is indicated by the probability between 0 and 1 under the outcome. The symbol “#” simply is the “leftover” probability, calculated by subtracting the other probabilities for that node from 1:
