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Outcome utilities– adjusting forthe quality oflife 205
Figure 10.9 shows Patient B’s utility for life with artificial speech, given these three answers to the assessment
question.
The outcome utilities plotted for 5, 10, and 25 years in Figure10.9 were determined directly from the expression
normal speech
For example, Patient B’s value for s
2
(10years) is 0.78 and according to the dotted curve in Figure10.9, the utility for a
10- year length of life with normal speech is 0.6409. Therefore,
tth normal speech
Live years with artificial speech10 07806409 0 4999
.. .
Similar calculations determine the utilities for living 5 and 25 years with artificial speech. The remainder of the utility
curve shown in Figure10.9 was drawn by interpolating between these three assessed values.
At first glance, the quality-
survival tradeoff model appears to require a different assessment process. However, a
quality- survival tradeoff model also can be inferred from the same questions used by the quality- lifetime tradeoff
model. More specifically, the minimum acceptable survival probabilities used by the quality- survival tradeoff model
can be determined from the length- of- life tradeoffs, the patient would accept to avoid a quality reduction. This equiva-
lence would be important for patients who find it easier to think about the quality of their life in terms of lifetime
reductions rather than survival probabilities.
For example, recall that the following are the lifetime reductions Patient B would accept in order to avoid the loss of
normal speech:
• 5 years with normal artificial equivalent to 5 years with normal speech
• 10 years with normal artificial equivalent to 7 years with normal speech
• 25 years with normal artificial equivalent to 12.5 years with normal speech
These three assessments mean that for Patient B
aal speech
Live years with artificial speechLiveye
10 7aars with normal speech
Live years with artificial spee
25 cch Live years with normal speech
U 12 5.
Consider the minimum acceptable survival probability with a lifetime of 10 years, which is denoted
2
10
. We just
saw that
U
Live years without normal speechLiveyears w10 10 10
2
iith normal speech
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1. 0
05
5.0 7. 010.0
10 15 20
25
Utility
Length of life (years)
Utility with artificial speech
Utility with normal speech
s
2
(25)×u(25)
u(t)
0.4999
0.6409
s
2
(5) × u(5)
s
2
(10)× u(10)
s
2
(5) = 1. 00
s
2
(10) = 0.78
s
2
(25) = 0.73
Figure10.9 Utility for length of life with artificial speech based on the quality- survival tradeoff model. Utility for length of life with normal speech is
shown as a dotted curve. The former (u(t)) is derived from the latter by multiplying u(t) by the corresponding survival probabilities (s
2
(t)). All utilities
have been scaled so that the utility for 25 years of life with normal speech is 1.0.
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206 Medical decision making
But
mmal speech
This means
2
nnormal speech
We can rearrange this expression as follows:
U
U
2
10
7
10
Live years with normal speech
Live years with noormal speech
The dotted curve in Figure10.9 shows Patient B’s utilities for length of life with normal speech:
.
.
Inserting these values into the expression for
2
10
yields
U
U
2
10
7
10
Live years and normal speech
Live years and normmal speech
0 4999
0 6409
0
7800
.
.
.
We can repeat this process to determine the values for s
2
(5) and s
2
(25). In other words, Patient B’s answers to the
quality-
lifetime tradeoff questions told us the minimum survival probabilities needed to use the quality- survival
tradeoff model to represent Patient B’s preferences.
The opposite also is true. Answers to the quality- survival tradeoff assessment questions imply the information
required to represent Patient B’s preferences with the quality- lifetime tradeoff model.
Therefore, the quality- survival tradeoff model has the same assessment process as the quality- lifetime tradeoff
model. This means that both assessment processes produce the same outcome utilities. This raises the question, why
consider the quality-
survival tradeoff model in the first place? The answer is found in the corresponding parametric
model for representing quality preferences by survival tradeoffs.
10.4.2 Parameterized quality- survival tradeoff model
The quality- lifetime tradeoff model discussed in the previous section adjusts for the quality of life by first reducing the
length of life. Utility is then determined for that reduced lifetime. In contrast, the quality-
survival tradeoff model starts
by determining the utility for the length of life, without the loss in quality. That utility is then adjusted to account for
the quality reduction caused by the symptoms or disabilities that are part of the outcome.
Given this comparison of the two models, recall that the parametric version of the quality-
lifetime tradeoff model
uses a fixed value ϕ
i
to quantify the length of life adjustment. That is, the utility for life in the i
th
quality state is approxi-
mated as follows
iUt
th
i
Live years in quality stateLiveyears in symptom
free quality state
where ϕ
i
is the average value for the ratio of the length of life in the i
th
quality state over the equivalent length of life in
a symptom- free quality state. Figure10.4 showed how this average was calculated.
On the other hand, the parametric version of the quality- survival tradeoff model uses a fixed value θ
i
to quantify the
utility adjustment. Recall that with the quality- survival tradeoff model the utility for life in the i
th
quality state is
istU t
th
i
Live years in quality stateLiveyears in symp
ttom free quality state
The parametric version of the quality- survival parametric model is the approximation:
iUt
th
i
Live years in quality stateLiveyears in symptom
free quality state
In other words, the parameter θ
i
approximates s
i
(t) by a constant.
Figure10.10 shows how the minimum acceptable survival probability for life with artificial speech varies with the length
of life. We denote these probabilities by
2
. The curve in Figure10.10 is based on Patient B’s assessed values for
2
.
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Outcome utilities– adjusting forthe quality oflife 207
Assuming Patient B can expect to live at most another 40 years, the average value for s
2
(t) has been calculated over
a 40- year period. The result is value of 0.79 for θ
2
. Figure10.11 compares the resulting parametric model to the quality-
survival tradeoff model based on the assessment of Patient B’s quality preferences. That is, the parametric version of
the quality- survival tradeoff model for Patient B is
t
th
Live years in with artificial speech
079.
Figure10.11 compares the values for this approximation to the utility model assessed for Patient B.
Figure10.12 compares the parametric utility model shown in Figure10.11 to the corresponding parametric model
based on the quality- lifetime tradeoff model. Both parametric utility models also are compared to the utility model
assessed for Patient B. Note that the quality- survival tradeoff model more closely matches the assessed utility for this
patient. This closer match is typical for comparisons of the two parametric models.
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
40
353025
s
2
(t)
Length of life with artificial speech (years)
Assessed values
Fitted curve
Average = 0.79
Figure10.10 Patient B’s minimum survival probabilities for avoiding loss of normal speech (s
2
(t)). The curve for lifetimes past 25 years are
determined by extrapolating the quality-
lifetime tradeoff function 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 assessed quality-survival tradeoff function
Utility for life with normal speech
Based on parametric quality-survival tradeoff function
Figure10.11 Utility for length of life with artificial speech determined using the parametric version of the quality- survival parametric model. The
grey curve is taken from Figure10.9 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 25 years of life with normal
speech is 1.0.
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208 Medical decision making
As before, the utility for symptom- free life can be represented by the exponential utility model described in Chapter9.
This leads to the following definition of the quality- survival parametric utility model:
tility for the life of lengthin thequality stateti
th
i
1
e
t
Notice that this utility model does not adjust for a loss in the quality of life by changing how the patient’s risk atti-
tudes are represented. The risk parameter γ is not changed. Instead, the quality reduction is represented by an overall
reduction in the utility for the outcome. Therefore, the problematic distortion of risk attitudes is avoided.
10.4.3 Parameterized quality- survival tradeoff model andexponential survival
As we did in the previous section, suppose that the uncertainty for the length of life is such that:
t
Survival
1
where t is the length of life and λ is the death rate expressed in the time units of t. With the quality- survival parametric
model, the expected utility for the outcome is:
xpected utility with exponential survival in the qualiti
th
yy state
i
where the term θ
i
is the patient’s quality- survival tradeoff parameter for thei
th
quality state and γ is the patient’s risk
parameter. As with the other quality tradeoff model, the complicated mathematics required to prove this result are not
shown here.
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)
Quality-lifetime parametric model
Quality-survival parametric model
Assessed utility
Figure10.12 Patient B’s assessed utilities for length of life with artificial speech compared with utilities determined by the quality- lifetime parametric
model and the quality- survival parametric model. All utilities have been scaled so that the utility for 25 years of life with normal speech is 1.0.
Definition: quality- survival parametric model
The quality- survival parametric model represents the utility for an outcome in which the patient will live for time t
in the i
th
quality state as follows:
tility for the life of lengthin thequality stateti
th
i
1
e
t
where γ is the patient’s risk parameter expressed in the time units of tand θ
i
is the quality- survival tradeoff
parameter for thei
th
quality state.
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Outcome utilities– adjusting forthe quality oflife 209
This means the quality- survival parametric model, when combined with the exponential utility model, provides a
simple expression for determining the expected utility for an outcome. As with the quality-
lifetime parametric model,
determining the expected utility requires one parameter for risk attitudes and one parameter for the quality state. The
discussion will now turn to how to determine values for those quality parameters.
10.5 What does it all mean?– anextended example
This chapter concludes the discussion of outcome utilities. Chapter8 introduced the concept of risk aversion and
showed how to represent this inevitable part of how patients view uncertainty by a von Neumann–Morgenstern utility
model. That chapter introduced utility models as mathematical expressions that measure the importance the patient
places on an outcome when there is uncertainty about the patient experiencing that outcome. We called those measures
the outcome utilities.
Chapter9 and the current chapter extended the theoretical concept of an outcome utility to establish a more practical
framework for analyzing clinical decision problems. Those extensions used parametric models to simplify the process
required to measure patient preferences by outcome utilities. To see the importance of parametric models, consider the
alternative of directly assessing the patient’s utilities for possible outcomes in a decision problem.
10.5.1 Direct approach tooutcome utility assessment
For example, suppose that a decision problem can be summarized as the choice between treatment or no treatment
when disease is either present or absent. The corresponding decision tree is shown in Figure10.13. Note that this sim-
ple problem has only four possible outcomes:
• No treatment and no disease
• Treatment and no disease
• Treatment and disease
• No treatment and disease
Result: quality- survival 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-
survival tradeoff for life in the i
th
quality state can be represented by the
parameter θ
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
Outcome
(A1)
No treatment
Disease present
Disease absent
No treatment and no diseas
e
1–P(D
+
)
P(D
+
)
1–P(D
+
)
P(D
+
)
(A2)
No treatment and disease
Treatment
Disease present
Disease absent
Treatment and no disease
(A3)
Treatment and disease
Figure10.13 Tree for decision between treatment or no treatment when disease is either present or absent. This decision tree is used to illustrate
direct approach to utility assessment.
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210 Medical decision making
Note that we have listed these outcomes in order of decreasing preference. For example, the treatment has no value
unless Treatment and disease is preferred to No treatment and disease. Similarly, this would not be an interesting
problem unless No treatment and no disease is preferred to Treatment and no disease. Otherwise, treatment would
always be chosen, regardless of the presence or absence of disease. Finally, we assume Treatment and no disease is
preferred to Treatment and disease because it usually is.
Given the order of preference, we can start the direct approach to utility assessment with the following reference
values:
10.
00.
Direct utility assessment then uses the standard gamble question to determine the patient’s utilities for the remain-
ing two outcomes. Figure10.14 shows the decision tree for this assessment question when applied to the outcome
Treatment and no disease.
Of course, a patient’s utility for the intermediate outcomes only can be assessed in the context of an actual disease
and an actual treatment. Therefore, suppose the disease is a myocardial infarction and the treatment is hospitalization.
Given this context, the patient’s utility for the outcome Treatment and no disease might be assessed using the follow-
ing question:
Suppose that you must choose between two alternatives. One alternative is to spend a few days in a hospital but to otherwise be
healthy. The other alternative is to stay out of the hospital but there is a probability that you are experiencing a myocardial infarction.
How large must the probability of a myocardial infarction be for you to choose the second alternative and be admitted to a hospital?
A similar question would be used to determine the utility for the outcome Treatment and disease.
The decision presented in the standard gamble assessment question (Figure10.14) looks almost as complicated as
the decision presented in the original decision (Figure10.13). The only difference is that the standard gamble question
involves three outcomes whereas the original problem involves four outcomes. Utility assessment only makes sense if
the patient can resolve the decision presented in Figure10.14 but not the decision presented in Figure10.13.
The one advantage of the direct approach to utility assessment is that the complexity of the standard gamble assess-
ment remains the same even when the number of possible outcomes in the original problem grows. In other words,
directly assessing the utilities for a decision problem with hundreds of possible outcomes still only requires an assess-
ment question involving three of the possible outcomes. Of course, this advantage is offset by the proliferation of
assessment questions the patient must answer. A decision problem with a dozen possible outcomes requires that the
patient remain focused during a dozen standard gamble assessment questions. Direct utility assessment quickly
becomes impractical when the complexity of the decision tree starts to match the complexity of an actual clinical
decision.
Moreover, direct utility assessment questions present the patient with a cognitive challenge. Think about the ques-
tion posed by the standard gamble assessment question in Figure10.14. Answering this question requires the patient
to balance how they feel about unnecessary treatment with how they feel about not treating a disease they might have.
Moreover, the patient must express how they balance these two concerns by providing a single value for a probability p.
This cognitive challenge increases as more treatments and possible disease states are included in the analysis. In other
words, the direct approach to utility assessment requires the patient to give meaningful answers to a large number of
hard- to- answer questions.
Uncertain outcome
Worse outcome
Best outcome
No treatment and no disease
No treatment and disease
Guaranteed outcome
Treatment and no disease
p
1–p
Figure10.14 Decision tree for the standard gamble assessment question that determines the utility for the outcome Treatment and no disease.
The value for p such that the uncertain outcome and the guaranteed outcome are equivalent is the patient’s utility for Treatment and no disease.
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Outcome utilities– adjusting forthe quality oflife 211
McNeil and her colleagues addressed these challenges by using a different approach in both of their two studies of
patient preferences. Consider their study of laryngeal cancer treatment. A patient with this treatment decision faces a
range of possible outcomes that differ according to the length of life and the quality of life. Direct utility assessment
would have required separate assessment questions for each possible length of life combined with each possible qual-
ity state.
Instead, McNeil and her colleagues characterized each outcome as a combination of two dimensions: (1) how long
the patient lives and (2) whether the patient would live that life with natural speech. They measured their volunteers’
preferences for each dimension separately. One set of assessment questions determined a volunteer’s utility for the
length of life in a quality state. Another set of questions determined the adjustments needed to those utilities to reflect
how the patient felt about the quality of life that would be experienced in a quality state.
Separating the assessment process according to the length of life and the quality of life reduced the cognitive chal-
lenge of answering the questions. The parametric models described in this chapter, and the preceding chapter, greatly
reduced the number of required questions. We saw that two approaches can then be used to combine the results of the
two assessment processes into a single expression for determining a patient’s outcome utilities for this decision
problem.
This chapter concludes with a demonstration. We will apply the concepts in this chapter and the preceding chapter
to the treatment decision faced by patients suspected of having a pulmonary embolism. The results will be used in a
later chapter that discusses the important concept of threshold probabilities.
10.5.2 Outcome utility assessment based onoutcome decomposition
A threshold probability marks the point where the possibility of a treatable disease justifies starting treatment. The
discussion of threshold probabilities in that later chapter will show how the potential harms and benefits of a treatment
interact to determine when the treatment should be started. In turn, outcome utilities play a central role in quantifying
those potential harms and benefits. The following discussion demonstrates how the decomposition approach can
determine the outcome utilities needed to establish a threshold probability.
The example of how to treat suspected pulmonary embolism illustrates the discussion in that later chapter. Timely
treatment with anticoagulants can save the patient’s life by dissolving the blood clot. Anticoagulants also can cause
intracranial hemorrhaging, which can lead to significant disability or death. Figure10.15 shows a decision tree repre-
senting this clinical dilemma.
The dilemma starts with the uncertainty about actual presence of the pulmonary embolism. That uncertainty is rep-
resented by chance nodes B2 and B4 in the decision tree. Without treatment, the patient can survive either because
there was no pulmonary embolism or because the body’s own clot- dissolving mechanisms have been successful. The
probability of death from untreated pulmonary embolism is assumed to be 0.5000 (node B3).
Definition: direct approach toutility assessment
The direct approach to utility assessment starts by identifying the best and worst possible outcome, which are
assigned the utility of 1.0 and 0.0, respectively. Separate standard gamble assessment questions are used to deter-
mine the utilities for each remaining outcome. The disadvantages of direct assessment are:
• Large number of assessment questions required for a complex decision problem.
• Cognitive challenge of comparing outcomes that combine multiple issue, such as the length of life and the
quality of life.
Definition: outcome separation approach toutility assessment
Utility assessment by outcome separation represents each possible outcome as combination of dimensions, such
as the length of life and the quality of life. The patient’s preferences for each dimension are measured separately.
The outcome utilities are determined by combining the preference measures for each of the dimensions compris-
ing an outcome. The disadvantages of direct assessment are the validity of the assumptions used to
• Simplify how preferences are assessed for an outcome dimension.
• Combine the preferences assessed for the outcome dimensions into an overall outcome utility.
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212 Medical decision making
Note that the decision tree ignores the possibility of residual damage after surviving an untreated pulmonary embo-
lism. Therefore, survival after an untreated pulmonary embolism is assumed to be equivalent to not having a pulmo-
nary embolism.
Treatment of a pulmonary embolism reduces the probability of death from the disease to 0.5000 (node B8). However,
the probability that treatment will cause a hemorrhagic stroke is 0.0100 (nodes B5 and B9). The probability of dying
from a hemorrhagic stroke from excessive anticoagulation is 0.5000 (nodes B6 and B10). Surviving a hemorrhagic
stroke will lead to either mild or severe disability (nodes B7 and B11). The probability of a mild stroke is 0.25 and a
severe stroke is 0.75. We assume here that the probabilities of treatment complications are the same regardless of
whether the patient had a pulmonary embolism.
The patient who survives faces life in the following three quality states:
1. No complications
2. Mild stroke disabilities
3. Severe stroke disabilities
The patient also faces the uncertainty of how long they will live if they survive the episode and uncertainty about
possible complications of treatment. Quantifying that uncertainty requires different survival models for the following
possibilities:
• The patient has no residual complications from the disease or treatment. For this case, the example will assume an
exponential survival model with the life expectancy of a 55- year- old woman (35 years).
• The patient spends the remainder of their life with mild disability from a stroke. Life expectancies between 30 and
32 years were reported for 50- year- old women with post- stroke disabilities classified on the modified Rankin Scale
as 0 or 1 (Shavelle etal.,2019). Therefore, this example will assume an exponential survival model with a life expec-
tancy of 30 years for this case.
(B1)
(B4)
(B3)
Die from PE
0.0200
No treatment
Treatment
Survive PE
0.8000
Severe stroke
0.7500
PE present
PE absent
1–P(D
+
)
1–P(D
+
)
P(D
+
)
P(D
+
)
Death
Death
Mild stoke
disabilities
Severe stoke
disabilities
No
complications
Death
Mild stoke
disabilities
Severe stoke
disabilities
No
complications
Death
No
complications
No
complications
Die from PE
0.2000
No ICH
0.9900
ICH
0.0100
Die from ICH
0.5000
Survive ICH
0.5000
Mild stroke
0.2500
PE present
PE absent
Survive PE
0.9800
No ICH
0.9900
ICH
0.0100
Die from ICH
0.5000
Survive ICH
0.5000
Severe stroke
0.7500
Mild stroke
0.2500
(B2)
(B5)
(B6)
(B8)
(B7)
(B9)
(B10)
(B11)
B
C
A
PE Pulmonary embolism
ICH Intracranial hemorrhage
Figure10.15 Decision tree for treatment of suspected pulmonary embolism. Branch probabilities for survival from pulmonary embolism and
central nervous system bleed are from published literature. Branch probabilities for death from central nervous system bleed and severity of stroke
were estimated by the author. The letters A, B, and C designate outcomes discussed in the narrative.
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Outcome utilities– adjusting forthe quality oflife 213
• The patient spends the remainder of their life with severe disabilities from a hemorrhage stroke. Life expectancies
between 7 and 25 years were reported for 50-
year- old women with post- stroke disabilities classified on the modi-
fied Rankin Scale as 2 or greater (Shavelle etal.,2019). Therefore, this example will assume an exponential survival
model with a life expectancy of 15 years for this case.
Determining the outcome utilities for this decision problem starts with assessing the patient’s utility for life with no
complications. This example assumes that an exponential utility model represents the patient’s utility for the length of
life. Recalling from the discussion in Chapter9, this assumption means the utility for a life of length t can be repre-
sented as follows:
e
t
1
The value for γ, which we call the risk parameter, can be determined by asking a question like the following:
Suppose that you have a disease that will cause your death, on average, in 15 years. Also suppose that if this disease were cured you
could expect to live, on average, another 35 years. If there is a risky treatment that will either cure your disease or cause your immedi-
ate death, how large would probability of surviving have to be for you to choose this treatment?
The choice of 15 and 35 years used in this wording of the question is arbitrary. The length of these average outcomes
can be adjusted to describe a scenario that fits the patient’s circumstances. The values used in the sample wording
shown earlier are based on a 55-
year- old woman’s life expectancy without complications (35 years) and their life
expectancy after surviving a severe stroke (15 years).
In general, this assessment question can be represented as the decision tree shown in Figure10.16.
As explained in Chapter 9, the following expression determines the value for the risk parameter γ (see
Subsection9.2.6):
pX X
p
AB
//1
1
where p is the answer to the assessment question shown in Figure10.16.
The example will assume that 0.13/year is the resulting value for γ. Given this assumption, the following expression
determines the utility for life of t years without complications:
e
t
Life of years without complications
1
0 1300
0 1300.
.
The usual assumption is that the value for the risk parameter is independent of the patient’s quality state. In other
words, we assume the patient would provide the same answer to the assessment question if their remaining life would
be lived in any of the quality states for the problem.
In order to determine the patient’s utility for life with those disabilities, we must adjust the expression to represent
the quality-
of- life reduction. How to make this adjustment depends on the quality tradeoff model we decide to use. For
the reasons discussed in the preceding section, we will use the quality-
survival tradeoff model. This model adjusts for
living with a disability by determining the minimum survival probability, the patient would be required to undergo a
hypothetical treatment that would either eliminate the disability or cause sudden death.
Uncertain outcome
Uncertain survival with
X
B
year life expectancy
Live 0 years
Guaranteed outcome
Uncertain survival with
X
A
year life expectancy
p
1–p
Figure10.16 Decision tree for the assessment question that determines the patient’s utility for the length of life.
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214 Medical decision making
Living with the disabilities of a mild stroke is one of the possible quality states faced by a patient with suspected
pulmonary embolism. The different ways a mild stroke can affect a patient’s life complicates the assessment of the
quality parameter for living in this quality state. The corresponding assessment question must describe a representa-
tive level of disability for a mild stroke. The following wording of the assessment question is based on the definition
of disabilities classified as level 1– or mild stroke– on the modified Rankin Scale:
Suppose that you will live the remainder of your life with some difficulties speaking and minor reductions in your mobility. Suppose
there is a risky treatment that could cause your immediate death. If this treatment is successful it will not change how long you will
live. However, you will no longer have difficulties with speaking and mobility. How large with the probability of surviving the hypo-
thetical treatment have to be for you to choose the treatment?
Figure10.17 shows the general form for this assessment question expressed as a decision tree. The patient’s answer
is what we called the minimum acceptable survival probability and is represented by the probability θ in Figure10.17.
In this example, we assume that the patient would require at least an 80% chance of surviving. Therefore, the answer
to this assessment question implies a value of 0.8 for the quality parameter θ.
Recall that the quality-
survival parametric model determines the utility for a lifetime of tyears in a health state by
the expression
iications
So far we have determined that
e
t
Life of years without complications
1
0 1300
0 1300.
.
and that when the quality state is living with a mild stroke
080.
Therefore,
e
Life of years with mild stroke disabilities
0 8000
1
.
00 1300
0 1300
.
.
t
A similar process determines the quality adjustments needed to express the patient’s utility for life with the severe
stroke disabilities. The parameter θ for this quality state is determined using the answer to an assessment question like
the following:
Suppose that you will live the remainder of your life with significant difficulties speaking as well as very limited mobility. These dis-
abilities will keep you from caring for yourself. Suppose there is a risky treatment that could cause your immediate death. If this
treatment is successful it will not change how long you will live. However, you will no longer have difficulties with speaking and
mobility. Independent living would again become a possibility. How large with the probability of surviving the hypothetical treat-
ment have to be for you to choose the treatment?
This example supposes that the patient’s answer to these questions imply a value of 0.3 for the quality parameter θ.
It would follow that
Life of years with severe stroke disabilities
0 3000
1
.
ee
t0 1300
0 1300
.
.
Risky outcome
Live t years without
loss in quality of life
Live 0 years
Guaranteed outcome
Live t years with
loss in quality of life
θ
1–θ
Figure10.17 Decision tree for the assessment question that determines the patient’s quality parameter for a given length of life.
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