intermediate values represent impaired health states (see Figure
5). For example, a person undergoing kidney dialysis could assess
her current well-being at 0.55.
The same methodology is applied to every member of a
group to determine the average utility, and then is applied to
other conditions that, when valued, produce a list of preference as follows:
0.00 < [u(condition)
1] < ... < u(conditionn) < 1.00
(without loss of generality, higher sub-indices correspond
to higher preference values).
The standard gamble method is a different matter. Here, individuals are presented with a pair of options (see Figure 6).
Under Choice A, two scenarios are possible: perfect health with
probability p, and death with probability
1 – p (the process by
which a person chooses between randomized events is known
as lottery). Choice B, on the other hand, represents the status
quo.
The QALY weight is the value of p that results in indifference
between choices A and B. That is, the value of p that satisfies
E[A] = E[B].
At some point between July 1, 2005, and June 30, 2006
(when his health was poor), Werther could have been asked
whether he preferred to live the rest of his life in that state
(Choice B) or participate in a lottery (Choice A) under which
he would have a 50 percent probability of full recovery and
a 50 percent probability of dying. Had Werther opted for
Choice A with those odds, he would have been asked the
same question using different probabilities: Would he take
his chances in a lottery that promises full recovery 49 percent of the time? Analogously, had Werther selected Choice
B when offered a 50 percent probability of total recovery, the
same question would be asked—but now with a 51 percent
probability. The process is repeated until Werther is indifferent between options A and B, and the value of p, the utility
score, is determined.
The same principle is repeated with other individuals to
calculate the average. The procedure is then applied to other
conditions to obtain a list of utilities:
u(condition1) = p1
u(condition2) = p2
...
u(conditionn– 1) = pn- 1
u(conditionn) = pn
Without loss of generality, the sub-indices can be arranged
—TABLE 1—
Example of the Trade-Off Method
Life
Expectancy
Time Trade-
Off
6. 6 0.7
29.0 3. 1
34.0 5. 9
40. 6 3. 6
... ...
14. 3 3. 1
1. 6 0.4
35. 3 6.0
50.0 5. 3
2,947.3 355.0
Person
1
2
3
4
...
97
98
99
100
Total/
Average
Utility
89.9%
89.1%
82.5%
91.0%
...
78.4%
75.7%
82.9%
89.3%
88.0%
—FIGURE 5—
The Rating Scale Method
Death = 0.0
Current State
Perfect Health = 1
—FIGURE 6—
The Standard Gamble Method
Perfect
( 1.00)
p
A
1 – p
Death
(0.00)
B
Current
Health
State
so that higher preference values correspond to higher sub-indices:
p1 < p2 < ... < pn- 1 < pn
Which of the three methods, time trade-off, rating scale,
and standard gamble, is the best? The answer is rooted in the
extraordinary work on game theory carried out by Princeton University Professors John von Neumann and Oskar
Morgenstern.
