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# Decision Tree Analysis: To Undergo or not to Undergo Surgery

Firm research data are not yet available to predict the likelihood of survival for this 50 year old man. If the internist tells this man that if he elects to avoid surgical treatment of the liver problem, chances of survival will be approximately as follows: only 60% chance of living for 1 year, a 20% chance of surviving for 2 years, a 10% chance for 5 years, and a 10% chance of living to age 58. She places his probability of survival beyond age 58 without a liver transplant to be extremely low.

The transplant operation however, is a serious surgical procedure. 5% of patients die during the operation, with an additional 45% dying during the first year. 20% survive for 5 years, 13% survive for 10 years, and 8%, 5%, and 4% survive, respectively, for 15, 20, and 25 years.

#### Solution Preview

Please see the attached file for the detailed decision tree analysis.

Without Surgical Treatment
Only 60% chance of living for 1 year
20% chance of surviving for 2 years
10% chance for 5 years
10% chance of living to 8 years (58-50)

Converting this into mathematical format:
Probability multiplied by Year(s) expected to ...

#### Solution Summary

The solution develops a decision, using the life expectancy of the patient, whether to undergo or not to undergo a liver transplant surgery.

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