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Selection andinterpretation ofdiagnostic tests 285
These observations have some important implications:
• When benefits are high and harms are low, we should be willing to treat even when the probability of the target
condition is well below the outcome of a coin flip. Recall the earlier case of treating an adolescent with a sore throat
with amoxicillin, a safe drug.
• When benefits are low and harms are high, we should be cautious about starting treatment unless we are quite
sure that the patient has the target condition. Getting more information, e.g., doing a biopsy of a lung mass may
be the best action, as in confirming a suspected cancer diagnosis.
• When the benefits equal the harms, the treatment threshold probability is 0.50. The benefits of most treatments
exceed their harms, which means the treatment threshold probability will often be less than 0.50.
Finally, as an example of what we have discussed in this section, consider the decision about when to give an antibi-
otic for suspected pneumococcal pneumonia. Antibiotics are generally safe for those who are not allergic to them and
usually cure pneumococcal pneumonia. With minimal harms and a large benefit, the treatment threshold probability
should be low. The conclusion: if you have a good reason to suspect pneumococcal pneumonia, you should start an
antibiotic.
13.3.3 Heuristics forsetting atreatment threshold probability
If asked, clinicians do have subjective treatment threshold probabilities. The author has given medical grand
rounds on the diagnosis and treatment of suspected PE to audiences of experienced clinicians. Anticoagulation, the
standard treatment for PE, is life- saving but sometimes leads to fatal bleeding. Early in these talks, he asked mem-
bers of the audience to write down the lowest probability of suspected PE at which they would give anticoagula-
tion, in effect disclosing their treatment threshold probability. Similar numbers of clinicians raised their hands for
each decile of probability from 10–20 to 80–90. Perhaps the wide range of threshold probabilities would have been
narrower if the clinicians had taken the following formal approach to formulating a treatment threshold
probability
for PE:
Think about the dangers of making a mistake: either treating when the patient does not have a PE or withholding
treatment when the patient does have a PE. Which mistake is worse, and why? How much worse? This line of thinking
may help you answer the following question:
“At what probability of PE would I be indifferent between treating and withholding treatment?”
Test the strength of your convictions: “Would I really be willing to withhold treatment if the probability of the disease was
just below my threshold probability? Would I be willing to treat if the probability of the disease were just above the
threshold probability?”
Looking beyond a purely subjective estimate, clinicians could use this relationship to guide their thinking:
p
H
HB
*
Note that the right side of this expression is a ratio. The denominator is the sum of the harms and benefits. But for
many treatments, the harms are much less than the benefits. Therefore, often we can approximate our expression for
the threshold probability as follows:
p
H
B
* ≈
This simple expression suggests that we can think about the threshold probability as reflecting the relative impor-
tance of errors of commission and errors of omission. What we call the harm of a test result measures the loss to a
patient when subjected unnecessarily to the treatment. Subjecting a patient to this harm would be an error of commis-
sion. What we call the benefit of a test result measures the gain to a patient from receiving the treatment when they
have the targeted disease. Withholding this benefit would be an error of omission.
Consider the following heuristic for determining a treatment threshold probability:
p
*
≈≈
Errors of comission
Errors of omission
Overtreatment
Unde
rrtreatment
If you think undertreatment is 10 times worse than overtreatment, your treatment threshold probability is 0.10.
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286 Medical decision making
13.3.4 Determining thetreatment threshold probability forpulmonary embolism– aformal approach
To illustrate the treatment threshold probability model, we will use suspected PE, a common high- stakes diagnostic
problem with a well- developed body of evidence. The estimated annual US death toll from PE is 100 000. The most
common findings leading to suspicion of PE are chest pain (typically sharp and increased by a deep breath), shortness
of breath, unilateral leg pain, tenderness, warmth, and swelling. A history of cancer, blood clots, and recent immobility
are common settings for PE.
The first step in a formal decision analysis is to construct a decision tree, as shown in Figure13.5.
D−A−: The patient who does not have a PE and does not receive treatment faces the outcome of Survival without
complications, the most desirable outcome state. The utility for this outcome is U(D
− A−).
D+A−: The chance node B3 represents the uncertainty faced by the patient who has a PE but does not receive treat-
ment. The expected value for this chance node is the outcome utility U(D + A−) that we will use in our treatment thresh-
old probability calculation. The expected utility at node B3 is p[survive PE]
× 1.0 +p[die of PE] × 0. The probability of
death from untreated PE is uncertain since treatment of PE has become mandatory. The death rate for untreated PE was
30% 60 years ago, but the general care of very sick patients has improved and patients are now more likely to survive.
This analysis assumes a 5% mortality rate for untreated PE. A sensitivity analysis (Figure13.17) appears in Section13.7.
D−A+: A similar calculation will determine the expected utility for chance node B5, which represents what happens
if the patient does not have a PE but is treated for PE. However, the outcomes of treatment are the same as when PE is
present: survive and leave the hospital or experience an intracranial hemorrhage (ICH) due to anticoagulation (chance
node B6). If they survive the ICH (node B6), they still face uncertainty about the severity of the stroke caused by the
bleed (node B7). The expected utility for chance node B5 is the outcome utility for the term U(D − A+).
D+A+: Determining the outcome utility for treated PE, U(D+A+) involves the branches originating at chance node
B8 in the decision tree. If PE is present, the patient may die of PE (chance node B8). The patient who survives the PE
(B1)
(B4)
(B3)
Die from PE
0.0050
No treatment
Treatment
Survive PE
0.9500
Severe stroke
0.75
PE absent
1–p(D+)
PE absent
1–p(D+)
PE present
p(D+)
PE present
p(D+)
Death
Death
(D + A +) Mild stoke
disabilities U = 0.7767
(D + A +) No
complications
Death
(D – A +) Mild stoke
disabilities U = 0.7767
(D – A
+) Severe stoke
disabilities U = 0.2419
(D – A +)No
complications
Death
(D + A –) No
complications
(D – A –) No
Complications)
Die from PE
0.0500
No ICH
0.9900
ICH
0.0100
Die from ICH
0.5000
Survive ICH
0.5000
Mild stroke
0.25
Survive PE
0.9950
No ICH
0.9900
ICH
0.0100
Die from ICH
0.5000
Survive ICH
0.5000
Severe stroke
0.75
Mild stroke
0.25
(B2)
(B5)
(B6)
(B8)
(B7)
(B9)
(B10)
(B11)
(D – A
+) Severe stoke
disabilities U = 0.2419
Figure 13.5 Decision tree for estimating the treatment threshold probability for pulmonary embolism. The initial decision node B1 represents the
decision whether to withhold or start treatment. The open circular chance nodes B2 and B4 represent the uncertainty about whether the patient
has had a PE. Note that node B2 leads to two states: D−A− and D+A− and Node B4 leads to D−A+ and D+A+.
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Selection andinterpretation ofdiagnostic tests 287
may leave the hospital or may experience an ICH, which will cause either death or a stroke. The outcome utility
U(D+A+) is the expected utility for chance node B8.
The branch probabilities for the decision tree shown in Figure13.5 and Table 13.1 are taken from two sources:
randomized trials of drugs to treat PE and DVT and observational data sets. The patients from these two sources may
differ. Participants in randomized trials of drugs are often selected to have few co-
morbid conditions that would cause
them to leave the study before experiencing a study endpoint. This analysis assumes that the PE-
related death rate is
0.5%, a figure taken from a community-
based observational data set of unselected patients with PE.
The remaining task is to determine the utilities for the possible outcomes in the decision tree. These are taken from
Chapter10 and are listed in Table13.2.
The worst outcome is death and the best outcome is survival without complications. The utilities for these two outcomes
are 0.0 and 1.0, respectively. With survival and no complications, the patient in our example would have the life
expectancy of a typical 55- year- old woman, an additional 35 years.
If the patient suffers a stroke due to ICH, she will face a reduced life expectancy and a reduction in the quality of her
life. The final section of Chapter10 used the example of the four outcomes in Table13.2 to show how to assess a
patient’s outcome utilities, taking account of the patient’s risk attitudes and preferences for the quality of their life. The
outcome utilities determined in that example are shown in Table13.2.
We now have what we need to calculate the expected utilities for the four outcome states. Table13.3 is based on the
decision tree (Figure13.5). In Table 13.3, probabilities are shown in normal font and utilities in boldface. Refer to
Figure13.5 for help in understanding the calculations.
The harm and benefit are:
H UD AUDA
UD AUDA
1 0000 0 9919 0 0081
0
...
.99870 0 9500 0 0370
..
Table 13.1 Probabilities for treatment decision for suspected pulmonary embolism.
Outcome Probability
Death with treatment for PE 0.005
Death with no treatment for PE 0.05
With treatment
Intracranial hemorrhage 0.01
Survival after intracranial hemorrhage 0.50
Mild stroke after surviving intracranial hemorrhage 0.25
Severe stroke after surviving intracranial hemorrhage 0.75
Survival without PE or treatment 1.0000
Table 13.2 Outcomes andutilities fortreatment decision forsuspected pulmonary
embolism.
Outcome Outcome utility
Death 0.0000
Survival with severe stroke 0.2419
Survival with mild stroke 0.7767
Survival with no complications 1.0000
Table 13.3 Path probabilities andutilities fordecision tree forsuspected pulmonary embolism.
Outcome Calculation Expected utility
U(D − A−)= +1.0000 × 1.0000= 1.0000
U(D + A−)= +0.9500 × 1.0000 + 0.0500 × 0.0000= 0.9500
U(D − A+)= +0.9900 × 1.0000 + 0.0100 × 0.5000 × 0.0000 + 0.0100 × 0.5000 × 0.7500 × 0.2419
+ 0.0100 × 0.5000 × 0.2500 × 0.7767 = 0.9919
U(D
+ A+)= +0.0050 × 0.0000 + 0.9950 × 0.9900 × 1.0000
+0.9950 × 0.0100 × 0.5000 × 0.0000 + 0.9950 × 0.0100 × 0.5000 × 0.7500 × 0.2419
+ 0.9950 × 0.0100 × 0.5000 × 0.2500 × 0.7767 = 0.9870
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288 Medical decision making
Accordingly, the treatment threshold probability is
p
H
HB
*
.
..
.
0 0081
0 0081 0 0370
0 180
This treatment threshold probability for PE may seem quite low. The rationale for treating PE when its probability
could be as low as 18% is straightforward: PE is a deadly disease, and while treatment has infrequent but serious
harms, it is very effective.
For the examples in this chapter, we will use p*=
0.18. It is a treatment threshold probability for PE, not the treatment
threshold probability. Section13.7 reinforces this point by showing how p* changes depending on the value of several
parameters in the decision tree in Figure13.5.
Readers should take the specifics of the examples as illustrative of how to use a treatment threshold probability to
guide clinical practice, not as a guide to the care of patients with PE. For the latter, clinicians should use evidence-
based
practice guidelines for managing PE.
13.4 Threshold probabilities fortesting
This chapter is about making the best of situations in which the benefits of treatment are accompanied by harms. In
clinical decision making under uncertainty, the approach to balancing the benefits of treatment against its harms is to
choose the action that maximizes the patient’s expected utility at the patient’s p[D]. The focus of this chapter has been
the treatment threshold probability (p*), which governs the Treat-
No Treat decision. Getting more information is the
clinician’s third option. The topic now shifts to choosing between taking no action, ordering a test, or starting
treatment.
13.4.1 The criteria fordoing atest
Criterion 1. Test when the pre-test probability is below the treatment threshold and the post-test probability after a
positive test would be above the treatment threshold
Criterion 2. Test when the pre-test probability is above the treatment threshold and the post-test probability after a
negative test would be below the treatment threshold:
The rationale for these criteria is Principle 1: seek more information if, and only if, a test result could change your plan.
Criterion 1 and Criterion 2 restate the teaching precept that you should do a test if and only if a test result could
change your management of the patient. This precept is easy to remember, but potentially difficult to use in practice
because it does not address the particulars of the patient’s situation. Ideally, the approach would include factors like
the effect of treatment, the patient’s probability of the target condition, the sensitivity and specificity of the test, and
how the patient feels about potential downstream health states. The next topic is a method that uses these factors to
inform the decision to do a test.
13.4.2 A method fordeciding when toperform adiagnostic test
The potential for treatment- related harm is a recurring theme in this chapter. The decision maker ’s goal is to optimize
the balance of harms and benefits at the patient’s probability of the target condition (Principle 4). The basic strategy for
optimizing care is to choose the option that maximizes the patient’s expected utility. In this section, we learn how to
make utility- maximizing decisions about when to get more information. The simple tree shown in Figure13.6 represents
the choice between do not treat, do a test, and treat.
Test
Tr eatment
No treatmen
t
Figure 13.6 Decision tree for choosing between no treatment, test, and treat.
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Selection andinterpretation ofdiagnostic tests 289
To decide between these three alternatives, we must calculate the expected utility of each option and act upon the
one with the highest expected utility at each probability of the target condition. Here is an opportunity to take a short-
cut. Instead of calculating the expected utility at each probability, we divide the probability scale into three zones, one
for No Treat, one for Test, and one for Treat. As with the treatment threshold probability (Section13.2), the action with
the highest expected utility will be the same within each zone: No Treat, Test, or Treat. On the probability scale, the
transition from the No Treat zone to the Test zone is a threshold probability, as is the transition from Test to Treat. If we
identify these two thresholds, we simplify the task of choosing between No Treat, Test, and Treat.
Figure13.7 depicts the outcomes of the Test option. The probabilities at the chance nodes that depict the outcome
ofthe test are written in conditional probability notation. For example, if the patient is diseased and the test is positive,
the probability of the test being positive is the conditional probability, p[T+|D+] (“probability of a positive test given
that the disease is present”), also known as the sensitivity (abbreviated as SE). To simplify the notation in the rest of
this chapter, we will use the abbreviations SE for sensitivity and SP for specificity.
Recall the following definitions from Chapters4 and5:
Target condition present Target condition absent
p[T+|D+]=sensitivity (SE) p[T−|D−]=specificity (SP)
p[T−|D+]=1 – sensitivity (1−SE) p[T+|D−]=1 – specificity (1−SP)
Using this notation, we may calculate the expected utility of the test option portrayed in Figure13.7. A+ denotes
Treat, and A– denotes No Treat, and we assume that the result of the test will determine the treatment.
pD UD ApDUDA
pD
1
11
SP SPUD Ap
DU
DA1
The equations for the expected utility of the No treat (A–) and Treat (A+) options are obtained by averaging out at
the chance nodes in the trees for these options (Figures13.8 and13.9, see next page). Similar equations were used ear-
lier in this chapter to derive the expression for the treatment threshold probability.
Utreat
ApDUDA pD UD A1
EU ApDUDA pD UD A1
T
est
p[D+]
p[T +|D +]
U [D + A
+]
U [D + A
–]
U [D – A
+]
U [D – A
–]
p[T –|D +]
T +
Tr eat
p[D–]
p[T +|D –]
T +
Tr eat
p[T –|D –]
T –
No treat
T –
No treat
Figure 13.7 Outcomes of the Test option.
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290 Medical decision making
Figure13.10 represents the equations for EU[Test], EU[A- ], and EU[A+] graphically by plotting the expected utility
of the decision alternatives (vertical axes) against p[D+], the probability of the target condition (horizontal axis). Each
of the lines intersects the vertical axes at a point determined by the utility of one of the disease- treatment states and, in
the case of the testing option, also by the SE and SP of the test. The points of intersection with the vertical axes deter-
mine the slope of the lines and, therefore, where they intersect. The points of intersection determine the testing thresh-
old probabilities.
To maximize the patient’s utility, the clinician should choose the alternative that has the highest expected utility at
each p[D+]. Figure13.10 shows that, given the slopes of the Test, Treat, And No Treat lines and the p[D+] where they
intersect, the preferred option depends on the probability of the target condition (p[D+]).
Low probability of the disease: Below a certain probability (the No Treat- Test threshold, pL), observation without treatment (No
Treat) has the highest expected utility. Below pL, the post- test probability after a positive test result would still be below the
treatment threshold probability (p*). Management would not change. Note that pL indicates the lower testing threshold.
No
Treat
p[D+]
U (D + A–)
U (D – A–)
p[D–]
Figure 13.8 Expected outcomes for the No treat option.
Tr
eat
p[D+]
U (D + A
+)
U (D – A+)
p[D–]
Figure 13.9 Expected outcomes for the Treat option.
Probability of disease, p[D+]
0.0 0.1 0.2 0.3
pL pUp*
0.4 0.5 0.6 0.7 0.8 0.9 1.0
U (D + A+)
U (D + A+)
U (D +
Test)
U (D – A–)
U (D – A+)
U (D – Test)
Utility
Treat
No treat
Test
Figure 13.10 Graphical representation of equations for EU[Test], EU[No Treat], and EU[Treat].
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Selection andinterpretation ofdiagnostic tests 291
High probability of the disease: Above a certain probability (the Test- Treat threshold, pU), treatment has the highest
expected utility. Above pU, the post-
test probability after a negative test result would still be above the treatment
threshold probability (p*). Management would not change. Note that pU indicates the upper testing threshold.
Intermediate probability of the disease: Between pL and pU, testing has the highest expected utility; the post-
test probability
could cross the treatment threshold and alter the decision to treat or not treat. Above p*, this outcome would require a
negative test result; below p*, it would require a positive test result.
To recapitulate, you should recommend, and the patient should prefer, the alternative with the highest expected util-
ity at the patient’s probability of the target condition (p[D+]). The uppermost lines in Figure13.10 represent the expected
utilities of the No Treat, Test, and Treat options at the probabilities of the disease for which they are the options with
the highest expected utility.
13.4.3 Equations forcalculating testing thresholds
We next derive expressions for calculating pL and pU. They are important because they define the zones of
probability at which No Treat, Test, or Treat has the highest expected utility and should be the preferred option at
the patient’s p[D].
If the patient’s initial pre- test probability of the disease falls below the No Treat- test threshold probability (pL), the
post- test probability after a positive test result (p[D+|T+]) would still fall below the treatment threshold (p*), and the
test result would not affect the decision to withhold treatment. If pL is the pre- test probability, the post- test probability
after a positive test is the treatment threshold probability. Note a key distinction: p* is a treatment threshold probability,
while pL is a testing threshold probability.
Referring again to Figure 13.10, when the probability of the target condition is above the Test- Treat threshold
probability (pU), Treat has the highest expected utility. Above pU, the post- test probability after a negative test result
would be above the treatment threshold probability (p*), and the test result would not affect the decision to treat. If pU
is the pre- test probability, the post- test probability after a negative test is the treatment threshold, p*.
Identifying the preferred action (do nothing, test or treat) simply requires knowing pL and pU and the pre- test
probability. The next step is to derive expressions for pL and pU as follows:
Definitions
pL: the No Treat- Test threshold probability
pU: the Test-
Treat threshold probability
In these abbreviations, p stands for probability and L and U stand for the lower (No Treat- Test) and upper
(Test- Treat) treatment threshold probabilities.
Definition
No Treat- Test threshold (pL): The minimum probability at which the Test option has the highest expected utility.
AtpL, No Treat and Test have the same expected utility.
Definition
Test- Treat threshold (pU): The maximum probability at which the Test option has the highest expected utility.
AtpU,Treat and Test have the same expected utility.
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292 Medical decision making
Recall the equations for solving the trees for the No Treat, Test, and Treat decisions:
1
pD UD ApDUDA
pD
1
1
11SP SPUD Ap
DU
DA
1
At the No Treat- Test threshold probability (pL) for p[D+], the expected utility of the “No Treat” option is, by defini-
tion, equal to the expected utility of the “Test” option. To determine pL, we set the right sides of the No Treat and Test
equations equal to each other and rearrange terms to obtain the following equation that can be solved for pL.
pL SP
UD AUDA UD A
UD A
1
11
UD AUDASP
This expression may be simplified by rearranging terms and substituting the following relationships:
H=U[D−A−] −U[D−A+], the harms of treating patients without the target condition
B=U[D+A+]
−U[D+A−] the benefits of treating patients with the target condition
The result is this equation: pL × (SE ×B)=(1−pL) × ([1−SP] ×H)
Solving this expression for pL
L
SP
SP SE
1
1
H
HB
Similarly, set the Test Equation equal to the Treat Equation and solve for pU
U
SP
SP SE
H
HB1
These equations for pL and pU do not contain p*, the treatment threshold probability, but they can be reformulated
in terms of p* which is related to H and B, the harms and benefits of treatment (from Section13.3). From the following
relationship, pL and pU may be obtained in terms of p*.
p
H
HB
*
This equation for p* can be solved for B, expressing B in terms of H and p*, and, similarly, solved for H. Substituting the
expressions for B and H in the preceding equations for pL and pU, we obtain the following relationships between p*
and pL and pU.
L
SP
SP SE
1
11
p
pp
*
**
U
SP
SP SE
p
pp
*
**11
Do these equations have face validity? Imagine an exceptionally good test whose SP and SE are both 1.0. For this test,
pL would be zero, and pU would be 1.0. Therefore, with a perfectly accurate test, testing would be preferred for all
pre- test probabilities.
To summarize, the derivation of the equation for pL is conceptually straightforward: set the expected utility of No
Test equal to the expected utility of Test and solve for pL. Likewise for pU: set the expected utilities of Test and Treat
equal to one another and solve for pU. The equations for pL and pU require only the sensitivity and specificity of the
test and the treatment threshold probability (p*). Of course, as we saw in the preceding section, setting p* is hard work.
However, when someone takes the next step– to represent the completed model in a computer– the effect of chang-
ing one or more of these parameters on pL and pU takes but a moment.
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Selection andinterpretation ofdiagnostic tests 293
13.5 Clinical application ofthe threshold model ofdecision making
13.5.1 Test selection forsuspected pulmonary embolism: anexample
We are now prepared to apply the threshold model to an important clinical problem: deciding when to test for suspected
PE. In Section13.3.4, we showed the process for determining a treatment threshold probability (p*) for PE. In our exam-
ple, p*= 0.18. We then derived equations for determining the two testing thresholds (pL, the No Treat- Test threshold,
and pU, the Test-
Treat threshold) that divide the probability scale into three zones: No Treat, Test, and Treat. These
equations require p* and the SE and SP of tests for PE.
In clinical practice, when PE is suspected, a typical first test is D- dimer, an inexpensive rapid test for blood clotting.
If indicated by the D-
dimer results, the second test is CT pulmonary angiography (CTPA), an expensive imaging test
for detecting a PE. Table13.4 shows their test performance characteristics. The sources for the SE and SP of the tests are
in the references list at the end of the chapter.
D-
dimer: The following equations determine pL and pU for D- dimer in suspected PE. In these equations, p* is 0.18.
L
SP
SP SE
1
11
056018
056018 1018
p
pp
*
**
..
.. .
095
0 115
.
.
U
SP
SP SE
p
pp
*
**
..
..11
044018
044018 10
.. .
.
18 1095
06
6
CT pulmonary angiography: CTPA would seldom be the first test in suspected PE: it is expensive, it uses radiocontrast
dye which can harm the kidneys, and it exposes the patient to considerable ionizing radiation. A high- quality multisite
study measured the SE (0.83) and SP (0.96) of CTPA in 2006.
LSPSPSE
111
004018
004018 1
ppp*/ **
..
..
0018083
0
011
..
.
U
SP
SP SE
p
pp
*
**
..
..11
096018
096018 10.. ..
.
18 1 0083
05
5
13.5.2 Incorporating aclinical prediction model into aprobabilistic framework fortest selection
forsuspected pulmonary embolism
This section describes a sequence of assessments, starting with the use of a clinical prediction model (the Wells criteria)
and followed by a blood test for blood clotting (D-dimer) and, if required, an imaging procedure (CTPA). Figure13.11
describes this sequence.
Table 13.4 Performance measures oftests forPE.
Test Sensitivity (SE) Specificity (SP)
D-
dimer 0.95 0.44
CT pulmonary angiogram 0.83 0.96
Wells Criteria
score
Do D-dimer
p[PE] = 0.37p[PE] = 0.11
p[PE|–] = 0.003
P[PE|+] = 0.23
>1≤1
Do D-dimer
T+
T–
p[PE] = 0.014 p[PE] = 0.06 p[PE] = 0.50p[PE] = 0.17
Do CTPADo CTPA Do CTPA Do CTPA
T+
T–
T+
T–
T+
T–
T+
T–
T+
T–
p[PE|–] = 0.035
P[PE|+] = 0.81
p[PE|–] = 0.01
P[PE|+] = 0.57
p
[PE|–] = 0.15
P[PE|+]= 0.95
Figure 13.11 Sequence of assessments for suspected pulmonary embolism.
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294 Medical decision making
The pre- test probability ofPE: theWells Criteria
When PE is suspected, the first step is to establish the patient’s p[PE] and then determine the zone it lies within (No
Treat, Test, Treat). The Wells Criteria is a well-
tested clinical prediction model for estimating p[PE].
Wells and colleagues identified 7 predictors of PE. Each has a weight of 1. With a score of 1 or zero, the p[PE] is 0.11.
With a score of 2 or more, the p[PE] is 0.37. These two probabilities (0.11 and 0.37) are the output of applying the Wells
Criteria. For the source, see the bibliography for this chapter.
When touse theD- dimer test after estimating thepre- test probability ofPE withthe Wells Criteria
If p* for PE is 0.18, pL for the D- dimer is 0.115, and pU is 0.66 (Table13.5). With a low Wells Criteria score (1 or zero),
the corresponding p[PE] is 0.11, which is just below the test zone for D-
dimer. Many clinicians would say “that’s close
enough to the Test range to be within the range of statistical uncertainty” and would do a D-
dimer.
0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
1.0
pL
pU
p*
TreatNo treat
Test range for D-dimer
T–
p[PE]
Probability of pulmonary embolism
T+
Wells
criteria ‘
score ≤1
Figure 13.12 Using the Wells Criteria to decide about doing a D- dimer. The blue bar denotes the Test range for D- dimer. To its left is the No Treat zone.
To its right is the Treat zone. Per the Wells Criteria, the p[PE] is 0.11, just below pL, which is 0.115. As discussed in the text, doing a D- dimer when the
p[PE] is this close to the Test zone is a reasonable decision. After a negative D- dimer, p[PE]=0.014, which is in the No Treat zone for D- dimer.
Table 13.6 Probability ofPE based onthe Wells Criteria andD- dimer results.
Wells criteria score p[PE] p[PE] after positive D- dimer p[PE] after negative D- dimer
1 or zero 0.11 0.17 0.014
≥2 0.37 0.50 0.063
Table 13.5 Test performance andtesting threshold probabilities forD- dimer andCTPA.
Sensitivity Specificity pL pU
D-
dimer 0.95 0.44 0.115 0.66
CTPA 0.83 0.96 0.011 0.55
With a Wells Criteria score of 1 or zero and a negative D- dimer, p[PE] becomes 0.014, which is below p* for treating
PE (0.18). Withholding treatment for PE in patients with a low Wells Criteria score and a negative D-
dimer test is a
common clinical practice based on the low rate of PE during several months of follow- up of such patients. Figure13.12
depicts the situation.
Use of D- dimer and CTPA in sequence after estimating the pre- test probability of PE with the Wells Criteria
The logical approach to diagnostic testing is to start with inexpensive, safe diagnostic tools and use more expensive
and potentially harmful tools if needed to make a treatment decision. The diagnosis of suspected PE illustrates this
sequential approach: apply the Wells Criteria, do a D- dimer if a result could change management, and do a CTPA only
when it could resolve uncertainty about whether treatment would maximize the patient’s expected utility.
The Wells Criteria score is≤1 As described in the preceding section, a low Wells Criteria score is an indication for
doing a D- dimer. Figure13.12 depicts the post- test p[PE] for a positive D- dimer (T+) and a negative D- dimer (T−).
Table13.6 lists the corresponding post- test probabilities after a D- dimer.
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