[Decision Trees] Consider the following situation:

The QALY weight for being dead is 0. The QALY weight for being perfectly healthy is 1.

A hospital has to decide whether to treat a patient for a difficult-to-diagnose disease.

There is a 70% chance that the patient is perfectly healthy, and a 30% chance that the patient has a fatal illness that will kill them within the next hour.

A treatment exists for the illness, but the treatment leaves any patient who takes it with permanent digestive problems. Living with these digestive problems has a QALY weight of 0.6.

If the patient is sick, there is an 80% chance that the treatment works, leaving the patient alive but with the permanent digestive problems mentioned above, and a 20% chance that the treatment fails, and the patient dies anyway.

If a healthy patient takes the treatment, they live, but suffer from the permanent

digestive problems mentioned above.

Simplifying assumptions: If the patient survives (is not killed in) the next hour, they will live for exactly 20 more years and then die (whether they are perfectly healthy or have digestive problems). There is no time discounting of QALY.

a. (6 marks) Draw a decision tree for the situation above using standard node symbols (squares, circles, triangles). Label all relevant probabilities and outcomes on your Decision Tree:

b. (6 marks) Use your decision tree to calculate the expected QALY from administering the treatment to the patient, and from NOT administering the treatment to the patient. Show your work. Should the hospital give the treatment to the patient? (You may assume the treatment is free or already paid for, so you only need to consider expected QALY.)

Expected QALY if the patient is treated: ___________

Expected QALY if the patient is NOT treated: ___________

Should the hospital treat the patient? Yes / No