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Outcome utilities– adjusting forthe quality oflife 195
because u(t) is the patient’s utility for living t years and living t years with artificial speech is equivalent to living w
2
(t)
years with normal speech. This would mean
2
In other words, we can combine the functions u(t) and w
2
(t) to determine a patient’s utility for any of the possible
outcomes of the laryngeal cancer decision.
A key step in applying this method is to determine a patient’s quality-
lifetime tradeoff function for life with artificial
speech w
2
(t). This is done using assessment questions similar to those used to determine the patient’s attitudes toward
risk. For example, the quality-
lifetime tradeoff function for life with artificial speech might be assessed by asking ques-
tions like the following:
Suppose you will live another t years. For the remainder of your life you will not have normal speech. Instead, your verbal communica-
tion will be limited to what can be achieved through the artificial methods that are available after your vocal cords have been removed.
How many years of life with artificial speech would you give up if doing so would mean that you could retain your normal speech?
Let x denote the patient’s answer to this question. It would follow that, for this patient
2
where t is the length of life with artificial speech posed in the assessment question. In the laryngeal cancer study, this
question was asked for values of t equal to 5, 10, and 25 years. The points labelled “assessed values” in Figure10.2
showed the responses for Patient B. For example, Patient B would be willing to give up3 years of life to retain normal
speech if otherwise they would live 10 years with artificial speech. This means that
2
10 7year
sy
ears
There is a hidden assumption in this approach that should not be overlooked. Recall that u(t) is the patient’s utility
for a symptom- free life lasting t years. Therefore, when we write
uw tyearswithartificialspeech
2
we are assuming that the risk attitudes toward the length of life are the same for life with normal speech as they are for
life with artificial speech. This may not be true for all patients. Some patients might feel very differently about risks
involving the length of life if they will live without normal speech. To allow for that possibility, we should determine
a different u(t) for each quality state. We can denote the utility for life in the i
th
quality state as follows:
i
th
utility for life lastingyears inqualitystate
This would mean the correct expression for the utility for life with artificial speech should be written
22
where u
2
(t) is assessed assuming life will be lived with artificial speech.
Mathematical expression: quality- lifetime tradeoff model
A quality- lifetime tradeoff model can be expressed using the following notation:
ti
i
th
Utility for lifetimeinquality stat
e
ti
i
th
Equivalent lifetimeinquality stat
e
Then
th
ii
years in quality state
Typically, the function u
i
(t) is assumed to be the same for all quality states.
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196 Medical decision making
Of course, multiple quality states each require corresponding versions of u
i
(t), which in turn requires multiple
assessment questions. These multiple assessment questions complicate the application of the quality- lifetime tradeoff
model. For this reason, quality-
lifetime tradeoff analysis typically assumes
ut ut
i
where u(t) reflects risk attitudes for some nominal quality state, such as living without symptoms or disabilities.
McNeil and her colleagues used this approximation when they determined the outcome utilities for the participants in
their study of laryngeal cancer. We will return to the implications of this approximation later in the chapter.
10.3.1 Parameterizing thequality- lifetime tradeoff model
The quality- lifetime tradeoff model provides an effective representation of quality preferences. However, the
mathematics used to compute an expected utility can be complicated. This section describes parameterized versions of
the quality-
lifetime tradeoff model that reduce that complexity.
Recall what we mean by a parametric model. These mathematical expressions can be adjusted to match something
like a patient’s outcome utilities by changing the values for a few elements in the expression. Those elements are the
expression’s parameters. In the previous chapter, we discussed the exponential utility model. This parameterized util-
ity model can be matched to the risk attitudes of a patient by adjusting the value for what we called the risk parameter
(γ). Our goal here is a similar simplification for the representation of quality preferences.
As a motivation for how we will develop a parametric quality-
lifetime tradeoff model, consider the ratio w
2
(t)/t.
Referring to Figure10.4, this ratio compares the length of life with artificial speech (t) to the equivalent length of life
with normal speech (w
2
(t)). Focusing on the three assessed values in Figure10.2
w
i
5
5
5
5
10
years
years
years
years
.
w
i
10
10
7
10
07
years
years
years
years
.
w
i
25
25
12 5
25
05
years
years
years
years
.
.
These ratios characterize the importance the patient places on avoiding the quality reduction with life in the i
th
qual-
ity state. The ratio is close to 1 if the patient places little importance on avoiding the quality reduction. The ratio is
much less than 1 if the patient places great importance on avoiding the quality reduction. Notice that for Patient B, the
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1. 0
0510 15 20 25 30 35
40
w
2
(t)/t
Length of life with artificial speech (years)
Average = 0.62
Assessed values
Fitted curve
w
2
(25)/25
w
2
(10)/10
w
2
(5)/5
Figure10.4 Ratio for the length of life with artificial speech (w
2
(t)) over equivalent length of life with normal speech (t). The values for w
2
(t) are from
Figure10.2. The value for the ratio, averaged over a lifetime of 40 years, is shown by the dotted line.
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Outcome utilities– adjusting forthe quality oflife 197
ratios vary from 0.5–1.0. However, the parametric quality- lifetime tradeoff model we will use ignores this variation
and treats the ratio w
i
(t)/t as a constant. In other words, the parametric quality- lifetime tradeoff model uses the
approximation
ii
where ϕ
i
is a single value for the ratio w
i
(t)/t.
Again, notice that the value for ϕ
i
should be close to one for quality states that involve mild symptoms or disabilities.
Living with these quality states is almost as good as symptom-
free life. At the other extreme, ϕ
i
should be close to zero
for a quality state involving highly painful or disabling symptoms. For this reason, ϕ
i
will be called the quality- lifetime
tradeoff parameter for thei
th
quality state.
As we have already seen, the utility for outcomes with a length of life spent in a quality state can be determined
by combining the utility for a length of life without symptoms (u(t)) and the quality-
lifetime tradeoff function w
i
(t).
That is,
wt
th
i
years in quality state
In other words, the utility for a life of a given length in a symptomatic outcome is the utility for its symptom- free,
but shorter, equivalent lifetime. With the parametric model, w
i
(t) is approximated by ϕ
i
× t. Using this approximation,
we have that
t
th
i
years in quality state
This expression for approximating the utilities for life in a quality state will be called the quality- lifetime parametric
utility model.
There are several methods for choosing a value for the quality- lifetime tradeoff parameter. The method we will
describe sets ϕ
i
equal to the ratio w
i
(t)/t averaged over the patient’s expected lifetime. For example, the average age
for the volunteers in the laryngeal cancer was 40 years. On average, someone who is 40 years old can expect to live
another 40 years. Figure10.4 showed how the ratio w
2
(t)/t varies in the case of Patient B’s quality- lifetime tradeoff
function for life with artificial speech. As noted in Figure10.4, the average value for the ratio w
2
(t)/t over a 40- year
lifetime is 0.62.
Therefore, based on the average value calculation shown in Figure10.4, we will use the following approximation to
represent Patient B’s quality preferences for life with artificial speech:
2
062
.
Figure10.5 compares the values for w
2
(t) that were assessed for Patient B and the quality- lifetime tradeoff function
approximation used in the parametric model. In effect, the parametric model approximates the curve for w
2
(t) by a
straight line with slope equal to the value chosen for ϕ
2
(0.62).
Figure10.6 compares (1) Patient B’s utility for life with artificial speech computed using the assessed quality- lifetime
tradeoff function and (2) Patient B’s utility for life computed using the parametric model. The outcome utilities based
on the assessed function have more credibility because they represent what Patient B actually said about their prefer-
ences. From this perspective, the parametric model underestimates the utilities for short lifetimes and overestimates
the utilities for long lifetimes.
Definition: quality- lifetime parametric utility model
Let w
i
(t) denote the quality- lifetime tradeoff function assessed for the i
th
quality state and let ϕ
i
equal the value for
the ratio w
i
(t)/t averaged over a suitable time period, such as the patient’s life expectancy. The quality- lifetime para-
metric utility model uses the following approximation to determine the patient’s utility for a life lasting t years on
the i
th
quality state:
t
th
i
years in quality state
The term ϕ
i
is called the quality- lifetime tradeoff parameter.
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198 Medical decision making
How significant are the differences between the two utility curves shown in Figure 10.6? As a starting point to
answering this question, we will consider how the two curves affect the resulting expected utilities calculated for two
of the laryngeal cancer treatments used in the study conducted by McNeil and her colleagues.
Of course, in order to calculate expected utilities for the two treatments, we need to have the corresponding prob-
abilities for the possible lengths of life after treatment. McNeil and her colleagues did not publish the surgery and
radiotherapy survival models they used; however, they reference an article that provides enough information to
estimate the survival curves for Stage III laryngeal cancer shown in Figure10.7 (Wang and O’Donald,1955).
Combining the lifetime probabilities implied by the survival curves in Figure10.7 with the assessed utility curves
shown in Figure10.3 results in the following expected utilities for the two treatments:
0
5
10
15
0510 15 20
25
Lifetime with normal speech (years)
Lifetime with artificial speech (years)
Slope = 0.62
Assessed values
Life with artificial speech (assessed w
2
(t))
Life with artificial speech (approximation 0.62 ×t)
Fitted to assessed values
Approximation
Figure10.5 Parametric approximation of the quality- lifetime tradeoff functions for artificial speech. The grey curve shows the quality- lifetime
tradeoff function fitted to the assessed values shown in Figure10.2.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1. 0
0510 15 20
25
Utility
Length of life (years)
Based on parametric quality-lifetime tradeoff function
Based on assessed quality-lifetime tradeoff function
Utility for life with normal speech
Figure10.6 Utility for length of life with artificial speech determined using the parametric version of the quality- lifetime tradeoff function
showninFigure10.5. The grey curve is taken from Figure10.3 and shows the corresponding utilities based on the assessed quality- lifetime
tradeoff function. For purposes of comparison, the utility for life with normal speech also is shown. All utilities have been scaled so that the utility
for 25years of life with normal speech is 1.0.
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Outcome utilities– adjusting forthe quality oflife 199
Therefore, assuming Patient B is a patient with Stage III laryngeal cancer who faces the survival curves shown in
Figure10.7,
1
they would prefer surgery over radiotherapy even though surgery will leave them with a life restricted to
artificial speech.
For purposes of comparison, Figure10.8 shows the survival curves for Stage I laryngeal cancer from the same study.
Combining the lifetime probabilities implied by these survival curves with the assessed utility curves shown in
Figure10.3 results in the following expected utilities for the two treatments:
1
The survival curves shown in Figure10.7 were derived from survival data observed in a population with an average age of 85 years consist-
ing of 95% men and 5% women. An actual analysis of this treatment decision would adjust these survival curves to match the average age of
40 years for the population studied by McNeil and her colleagues.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1. 0
0510 15 20
45
40353025
Probability survival ≤ t years
Length of life, t (years)
Surgery
Radiotherapy
Figure10.7 Estimated surgery and radiotherapy survival models for Stage III laryngeal cancer for a 58- year- old patient. These survival curves are
derived from data reported in 1955 for a study of laryngeal cancer treatment. Adapted from Wang and O’ Donald, (1955).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1. 0
0510 15 20
45
40353025
Probability survival ≤ t years
Length of life, t (years)
Surgery
Radiotherapy
Figure10.8 Estimated surgery and radiotherapy survival models for Stage I laryngeal cancer for a 58- year- old patient. These survival curves are
derived from data reported in 1955 for a study of laryngeal cancer treatment. Adapted from Wang and O’Donald, (1955).
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200 Medical decision making
Notice that the expected utilities have increased, which is reasonable since it is better to have Stage I cancer than
StageIII cancer. However, the expected utility for radiotherapy increased more than the expected utility for surgery.
Therefore, assuming Patient B is a patient with Stage I laryngeal cancer who faces the survival curves shown
in Figure 10.7, Patient B now would prefer radiotherapy over surgery. That switch is because the advantage of
radiotherapy – avoiding a life restricted to artificial speech – now is enough to overcome the survival advantages
ofsurgery.
Table 10.3 shows the results of repeating these expected utility calculations using the quality-
lifetime parametric
utility model. Results for both Stage I and Stage III laryngeal cancer are shown. The expected utilities calculated for
radiotherapy are the same for both methods because this treatment does not result in loss of normal speech. Therefore,
the outcome utilities are the same with the assessed utilities and the utilities determined by the parametric model.
Table10.3 shows that the discrepancy between the modeled utilities and the assessed utilities affects the decision
analysis. The expected utilities calculated for surgery using the parametric model differ from those calculated using
the assessed utilities. For example, with Stage I cancer, the expected utility for surgery is 0.6112when calculated using
the assessed utilities. This expected utility changes to 0.6538when the parametric utility model is used. However, the
change is not enough to alter that radiotherapy is preferred by Patient B for this cancer. A similar statement applies to
Stage III cancer.
Therefore, at least for this example, the expected utility changes caused by use of the parametric model does not
change the conclusions for how Patient B compares the two treatments.
10.3.2 Quality- lifetime parametric utility model withconstant risk attitudes
So far the parametric model we have discussed has not delivered on the promise of a simplified method for computing
an expected utility. The expected utilities shown in Table10.3 were calculated by determining the probabilities for each
possible length of life. Each of those probabilities were then multiplied by the corresponding outcome utilities and the
products summed over all possible lifetimes to determine the patient’s expected utility. In short, determining the
expected utilities was not a simple calculation.
We now will turn to additional properties of the quality- lifetime parametric utility model that will fulfill the promise
of simpler calculations. Those additional properties arise from the combination of the quality- lifetime parametric
model we have just discussed with the exponential utility model discussed in the previous chapter.
Recall that the exponential utility model is a mathematical expression that can quantify how a patient feels about
risk. When certain assumptions about how the patient views risk apply, that patient’s utility for length of life can be
expressed by the following mathematical expression:
t
1
We called γ in this expression the risk parameter because it quantified the patient’s risk attitudes for the length of
their life. In Chapter9, we saw several approaches for assessing a patient’s value for the parameter γ.
Assessing the value for γ in the context of symptom- free life means that the exponential utility model becomes the
patient’s utility for symptom- free life. That is, using the notation from earlier in this section:
t
1
As we just saw, the parametric version of quality- lifetime tradeoff function assumes
ii
Table10.3 Comparison of surgery and radiotherapy as treatment for Stage I and Stage III laryngeal cancer based on life expectancy and expected
utility calculations. Two expected utility calculations are shown. The columns labelled “Assessed” show the expected utilities calculated using the
assessed outcome utilities shown in Figure10.3. The columns labelled “Parametric” show the expected utilities calculated using the quality-
lifetime parametric utility model shown in Figure10.6.
Treatment
Stage I laryngeal cancer Stage III laryngeal cancer
Life expectancy
Expected utility
Life expectancy
Expected utility
Assessed Parametric Assessed Parametric
Surgery 20.2 years 0.6112 0.6538 13.0 years 0.4298 0.4362
Radiotherapy 18.6 years 0.7409 0.7409 6.5 years 0.2968 0.2968
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Outcome utilities– adjusting forthe quality oflife 201
That is, t years in the i
th
quality state is equivalent to ϕ
i
× t years in the symptom- free quality state. Therefore, combin-
ing the exponential utility model with the quality-
lifetime parametric utility model produces an expression with two
parameters.
iuwt ut e
th
ii
t
i
years in quality state
1
One parameter (γ) accounts for risk attitudes and the other parameter (ϕ
i
) accounts for quality preferences. The result
is a simple expression for outcome utilities that can be matched to the patient’s observed preferences for risk and qual-
ity by adjusting two parameters γ and ϕ
i
.
For example, recall that Patient B’s utilities for life with normal speech was shown in Figure10.1 as an exponential
utility model with risk parameter γ equal to 0.0815/year. Earlier, in this chapter, we determined that 0.62was Patient
B’s value for the quality parameter ϕ
2
. Therefore, Patient B’s utilities for life with artificial speech can be expressed:
t
years with artificial speech
11
2
0 0815 062
..ttt
e
1
0 0505.
The computational advantage of using this parametric model occurs when the uncertainty about how long the
patient will live can be expressed by an exponential survival model. The exponential survival model will not be dis-
cussed in detail until the next chapter. However, recall that with an exponential survival model
t
Aliveattime
1
where the parameter λ measures the probability of death during a unit of time. In the previous chapter, we saw that
with the exponential utility model, when the uncertainty about the length of life can be represented by an exponential
survival model, the expected utility can be determined by the simple expression:
xpected utility
1
A similar expression can be used to determine expected utility with the quality- lifetime parametric utility model. In
this case, the expected utility when the uncertainty about the length of life can be represented by the exponential sur-
vival model is
xpected utility
i
i
where ϕ
i
is the quality- lifetime tradeoff parameter for the i
th
quality state.
Result: quality- lifetime parametric utility model withconstant risk attitudes
Assume that utility for length of symptom- free life can be expressed as an exponential utility with risk parameter γ.
Also assume that the quality- lifetime tradeoff function for the the i
th
quality state can be expressed by the quality
parameter ϕ
i
. The quality- lifetime parametric utility model can then be expressed:
th t
i
1
Result: quality- lifetime adjusted utility withexponential survival
Suppose that (1) the patient’s preferences for length of life can be represented by an exponential utility model with
parameter γ, (2) the patient’s quality- lifetime tradeoff for life in the i
th
quality state can be represented by the
parameter ϕ
i
, and (3) the uncertainty for the length of life in an outcome can be represented by an exponential
survival model with parameter λ. The patient’s expected utility for that outcome is then:
i
i
Outcome
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202 Medical decision making
Therefore, when combined with the exponential utility model, the quality- lifetime parametric model can provide an
efficient representation of a patient’s utility for the outcomes they face in a decision problem. The resulting utility
model requires one parameter to quantify risk attitudes for the length of life and one parameter for each of the possible
quality states in the problem.
10.3.3 Quality- lifetime tradeoff models andrisk aversion– afly inthe ointment
Recall the expression we have just derived for the quality- lifetime parametric model. This expression is:
th t
i
1
where γ is the patient’s risk parameter expressed in the time units of tand ϕ
i
is the quality- lifetime tradeoff parameter
for thei
th
quality state. The parameter ϕ
i
quantifies how much the individual would be willing to shorten their life to
avoid living with the symptom or disability that defines the quality state. Therefore, in the case of a quality-
reducing
symptom or disability ϕ
i
always is less than one.
We also have an exponential utility model for the length of symptom-
free life which can be written
te
t
1
However, suppose that we let γ
i
denotes the product γ × ϕ
i
. We can then rewrite the expression that determines the
utility for life in thei
th
quality state as follows
th t
i
1
Notice that the value of γ
i
must be less than γ because ϕ
i
is less than one. But then this rewritten expression can be
thought of as simply an exponential utility for life spent in thei
th
quality state. That exponential utility model has a risk
parameter value of γ
i
, which is less than the risk parameter for the utility of symptom- free life.
Back in Chapter9, we noted that the value of the risk parameter γ decreases as risk aversion decreases. Therefore, the
mathematics of the quality-
lifetime parametric model implies that risk aversion for life in a quality state must decrease
as the importance of avoiding that quality state decreases. Perhaps it is true that for some patients, risk aversion
decreases when the quality of their lives decrease. But risk aversion is innate in how we perceive risk. It is troubling to
have that change in risk aversion dictated by the mathematical structure of the utility model.
This problematic mathematical property is one reason for considering the alternative to the quality-
lifetime tradeoff
model that will be discussed after we first consider a nontechnical controversy involving the use of these analytic tools.
10.3.4 Quality- lifetime tradeoff modelling andhealthcare policy analysis
Before considering an alternative to the quality- lifetime tradeoff model, a comment should be made about the
widespread use of life length adjustment techniques in health care policy analysis. Starting in the late 1960s, healthcare
policy analysis began using a concept known by the acronym QALY to incorporate quality of life concerns. QALY
stands for quality- adjusted life years. As the name suggests, QALY analysis adjusts the number of years an individual
might live according to the quality of life experienced during those years. Therefore, mathematically a QALY is equiva-
lent to the quality- lifetime tradeoff model described in this chapter. In recent years, QALY- based analysis has gener-
ated considerable controversy.
The idea behind the use of QALYs is that healthcare programs should promote the quality of life as well as the length
of life. Using QALYs to adjust the total number of years lived by the members of a population reflects this idea. For
example, consider an analysis of two programs, Program A and Program B. Suppose that both programs will result in
similar life expectancies for the targeted population. Also suppose that Program A increases the time people spend ina
preferable quality state. Adjusting length of life calculations to account for this quality difference provides a way to
understand the differences between the two programs.
Result: quality- lifetime tradeoff model andrisk aversion
The quality- lifetime tradeoff model implies that risk aversion decreases as the quality of life decreases. With the
quality- lifetime parametric model, an individual’s risk aversion for life with a symptom or disability is γϕ
i
where
γ is the individual’s risk parameter and ϕ
i
is the quality- lifetime tradeoff parameter, which must be less than 1.
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Outcome utilities– adjusting forthe quality oflife 203
In particular, suppose Program A helps prevent the development of diabetes whereas Program B improves survival
after the onset of diabetes. Recall the assumption that both programs result in similar life expectancies. But Program A
also increases the time spent without the treatment burden and disability associated with diabetes once it occurs.
When choosing between these two programs QALY-
based analysis would favor Program A over Program B.
However, consider the impact of choosing between these two programs from the perspective of individuals with
diabetes. Choosing Program A might make sense based on the total resulting QALYs. But that choice puts individu-
als with diabetes at a disadvantage since Program A provides no benefits for this subpopulation. Resolving the
inegalitarian implications of policy choices like this remains an important controversy in the field of healthcare
policy analysis.
10.4 Quality- survival tradeoff models
This chapter focuses on measuring a patient’s concerns about the symptoms and disabilities they might face. A mean-
ingful analysis of a patient’s decision must account for those concerns. The previous section described an approach
that measures how the patient feels about the quality of their life by asking how much the patient would be willing to
shorten their lifetime to avoid a loss of quality. The greater the importance the patient places on avoiding that quality
loss, the greater the length-
of- life tradeoff they would accept to avoid that reduction. Accordingly, that approach was
called the quality- lifetime tradeoff model.
The quality-
lifetime tradeoff model works reasonably well except for distortions caused by an implied assumption
that risk aversion changes when the quality of life is reduced. Those distortions increase as the quality reduction
caused by a symptom or disability worsens. The current section describes an alternative approach to analyzing quality
preferences that avoid this problematic assumption. The alternative that will be described has a parametric model that
retains the computational simplicity of the quality-
lifetime parametric model but can more closely match the patient’s
actual outcome utilities.
Once again, consider a disability such as the loss of normal speech. Another measure of how the patient feels about
the loss of normal speech is to propose a hypothetical treatment that could restore normal speech but could also cause
immediate death. A patient who places great importance on having normal speech would choose the hypothetical
treatment even if the probability of survival is low. A patient who places less importance on normal speech would
require a higher survival probability for that hypothetical treatment.
The minimum acceptable survival probability for avoiding a quality- of- life reduction is the key concept in this sec-
ond approach to measuring quality preferences. The greater the importance placed on avoiding the reduction the
lower the acceptable survival probability. In other words, this approach measures quality preferences by the survival
tradeoff that would be acceptable to the patient. Therefore, we will call this survival-
based approach to measuring
quality preferences the quality- survival tradeoff model.
The quality- survival tradeoff model can be represented by the following standard gamble assessment question:
Live 0 years
equivalent to
s(t)
1–s(t)
Live
t years with
quality-of-life loss
Live t
years without
quality-of-life loss
The gamble on the right is preferred if the probability of surviving is greater than s(t). The guaranteed outcome on
the left is preferred if the probability of surviving the gamble is less than s(t). Note that length of life (t) is included
because the acceptable survival probability may depend on how long the patient will live.
Scaling outcome utilities so that the utility for immediate death is zero, the equivalence in this standard gamble
assessment question leads to the following mathematical expression for the utility for life with the disability:
t
st U
tLive yearswith
quality of life loss
Live years
without
quality of life loss
Live years
10
st U
st U
t
st
Live years without
quality of life loss
1
0
st U
tLive years without
quality of life loss
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204 Medical decision making
How does this expression compare to the corresponding expression used with the quality- lifetime tradeoff model?
Recall that with the quality-
lifetime tradeoff model, the corresponding expression for living t years with a quality- of-
life loss is
t
U
wt
Live years with
quality of life loss
Live years
wwithout
quality of life loss
The term w(t) is a value less than t representing how much the patient would be willing to shorten their life in order to
avoid the loss in quality.
In other words, the quality-
lifetime tradeoff model adjusts for quality by reducing the length of life. In contrast, the
quality-
survival tradeoff model adjusts for living with a quality loss by directly reducing the utility for the length of
life. This difference may seem subtle; however, we will see that it avoids the fly-
in- the- ointment mentioned for the
quality-
lifetime tradeoff model.
10.4.1 Assessing quality preferences withthe quality- survival tradeoff model
Consider life without normal speech. The following question can be used to assess s
2
(t), which measures a patient’s
quality preference for loss of normal speech in the quality-
survival tradeoff model.
Suppose you will live another t years. For the remainder of your life you will not have normal speech. Instead, your verbal commu-
nication will be limited to what can be achieved through the artificial methods that are available after your vocal cords have been
removed. What survival probability would you require for a risky treatment that could restore normal speech but could also cause
your immediate death?
The answer to this question is the value for s
2
(t). This question can be represented by the following standard gamble
assessment question:
s
2
(t)
1–s
2
(t)
Live 0 years
equivalent to
Live
t years with
artificial speech
Live t
years with
normal speech
Once again, we call s
2
(t) the minimum acceptable survival probability for avoiding life with artificial speech. If we
scale utility so that a life of 0 years has the utility of 0.0, notice that the equivalence in this diagram can be expressed
mathematically as
st UtLive years with artificial speechLiveyears with
normal speech
Suppose the assessment question was asked with t equal to 10 years and assume Patient B answered with a probability
of 0.78. This means that for Patient B
2
10 078years
.
Similarly, suppose that Patient B answered with a probability of 0.73when t is equal to 25 years. Then
2
25 073years
.
Finally, if faced with a lifetime of 5 years or less, we will assume Patient B would require that survival be certain for a
treatment that would preserve normal speech. This means
2
5100years
.
Definition: quality- survival tradeoff model
A quality- survival tradeoff model represents the utility for an outcome that has a given length of life, and a quality-
reducing disability, by determining the minimum probability of survival, without the disability, the patient would
accept in order to avoid the disability. The utility for the original outcome with the disability is that minimum
survival probability multiplied by the utility for living the same length of life free of the disability.
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