Liver failure significantly reduces the quality of life for sufferers. Government studies indicate that patients with liver failure are equally happy living five years completely healthy or ten years with the disease. Hospital bills average $15,000/year for a person suffering from liver failure. After a transplant, patients recover to 90% of full health. With a successful liver transplant, patients will live 4 years with 100% certainty, and then die before year 5. Without the transplant, the patient will be alive after 1 year with probability .9 and after year 2 with probability .8. The patient will be dead in year 3 with no transplant. The cost of the transplant is $100,000 immediately. Each year the patient must take auto-immune suppressants that cost $10,000 to stop the body from rejecting the transplant. Even with the best surgeons the surgery is dangerous: 15% of patients do not have a successful surgery and die during the transplant (i.e. there is an 85% chance they will get the QALY's as described above, and a 15% chance they get Zero QALY's with the surgery). Use a discount rate of 5% throughout.

1. What are the implied quality weights for years 1, 2, 3, and 4 without surgery? With surgery? What are the probabilities of being alive in years 1, 2, 3, and 4 without surgery? With surgery?
2. How many QALY's can the patient expect to live if they do not have the surgery? What is the expected value of the QALY's if the patient has the surgery?
3. What is the present value of the cost of the surgery and follow-up treatment?
4. What is the ICER between the surgery and no surgery options?