The problem with representing outcome states by the life expectancy of people in the state is that life in one outcome state isn't necessarily equivalent to life in another state. For example, a person might be willing to trade one year of taking medication that causes mild nausea for 10 months of being in perfect health.

Representing a person's feelings about being in a health state is important. To represent those feelings in a decision tree, you must use a number. There are several methods for eliciting a number that represents a patient's attitude toward being in a health state:

• Standard reference gamble -This method is the most theoretically sound but the most difficult to do in practice. Standard reference texts describe this method.
  
  
• Time trade-off - This method involves asking the patient the smallest amount of time in a perfect health he would trade for his life expectancy in an undesirable health state. Typically, the person might say that he would trade 20 years in an undesirable health state, such as chronic chest pain, for 18 years in perfect health. The ratio of the smaller number to the larger number is the patient's utility for the health state, 0.9 in this case.
  
  
• Category scaling - This approach is the easiest. One simply asks the patient to represent his health state by making a mark on a scale bounded to zero on one end and 1.0 on the other.
  
  
• QALY - The most popular way to express an outcome state is by the quality-adjusted life years in the state (abbreviated QALY).

When using QALY in a decision tree, the horizontal box that represents a terminal node would contain two numbers: the patient's life expectancy in the state, and the patient's utility for the state. The product of these two numbers is the number of quality-adjusted life years the patient will spend in the state.

Problem 2.4.1

Now, consider how to assign utilities in the case study scenario. The injured rock climber faces several possible actions and that will lead to several health states. The rock climber will experience only one of them. The possible outcomes or health states for the rock climber are summarized in the table below:

Click to review rock climber's possible outcomes

The first step is to assign utilities of 1.0 to the best state and 0 to the worst state. The best state (1.0) is to save the climber's foot by treating the infection. The worst state (0) is death.

Now, putting yourself in the position of the rock climber, use the time trade-off method to decide on his utilities for the other health states. Think how many years in perfect health would be equivalent to ten years in each particular health state. The ratio of these two numbers is the utility.

Question 2.4.1

Suppose you think that the climber would trade 9 years in perfect health for ten years with a prosthetic foot. What would be his utility for ten years with a prosthetic foot?

	90
	9.0
	0.9
	1.1

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