# Question: Dr Switzer has a seriously ill patient but has had

Dr. Switzer has a seriously ill patient but has had trouble diagnosing the specific cause of the illness. The doctor now has narrowed the cause down to two alternatives: disease A or disease B. Based on the evidence so far, she feels that the two alternatives are equally likely.
Beyond the testing already done, there is no test available to determine if the cause is disease B. One test is available for disease A, but it has two major problems. First, it is very expensive. Second, it is somewhat unreliable, giving an accurate result only 80 percent of the time. Thus, it will give a positive result (indicating disease A) for only 80 percent of patients who have disease A, whereas it will give a positive result for 20 percent of patients who actually have disease B instead. Disease B is a very serious disease with no known treatment. It is sometimes fatal, and those who survive remain in poor health with a poor quality of life thereafter. The prognosis is similar for victims of disease A if it is left untreated. However, there is a fairly expensive treatment available that eliminates the danger for those with disease A, and it may return them to good health. Unfortunately, it is a relatively radical treatment that always leads to death if the patient actually has disease B instead. The probability distribution for the prognosis for this patient is given for each case in the following table, where the column headings (after the first one) indicate the disease for the patient.
The patient has assigned the following utilities to the possible outcomes:
In addition, these utilities should be incremented by –2 if the patient incurs the cost of the test for disease A and by –1 if the patient (or the patient’s estate) incurs the cost of the treatment for disease A.
Use decision analysis with a complete decision tree to determine if the patient should undergo the test for disease A and then how to proceed (receive the treatment for disease A?) to maximize the patient’s expected utility.

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