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Selection andinterpretation ofdiagnostic tests 295
Low Wells Criteria score and D- dimer negative: After these findings, the post- test probability of PE is 0.014. What is the
next step? Do nothing or do a CTPA? The p[PE] of 0.014 is just above pL for the CTPA (pL=0.011). Therefore, doing a
CTPA would be a utility- maximizing decision. After a positive CTPA (T+), the p[PE] would be 0.23, which is above p*
for pulmonary embolism (p*=
0.18). After a negative CTPA, p[PE] would be 0.003. Figure13.13 shows this sequence of
events, and Table13.7 shows the post-
test probabilities of PE for the CTPA result.
Discussion: Current clinical practice would be to observe the patient without treating them after a low Wells Criteria
score and a negative D- dimer. Why, when the p[PE] is 0.014, might doing a CTPA have the highest expected utility of
the alternative actions? What are the consequences of Do nothing, Test, or Treat in this situation?
As a reminder, when reading about the three alternatives: with a probability of 0.014, the diagnosis remains uncer-
tain, which means that any action (Do nothing, Test, or Treat) has potential harms or benefits.
Alternative 1: Start treatment. Treating when the probability of PE is 0.014would mean giving anticoagulation to everyone in a
population in which only 1.4 persons per 100would have the target condition and could benefit. The other 98.6 per 100would not
have the target condition, could not benefit, and might be harmed by treatment. Given concerns about ICH because of anticoagula-
tion, treating would seem imprudent.
Alternative 2: Do a CTPA and start treatment if it is positive. The probability of a positive CTPA would be 0.05. If the CTPA were
positive, the post- test p[PE] would be 0.23. Compared with Alternative 1, 23 persons per 100 treated would have the target condition
and could benefit from treatment. Conversely, 77 per 100with a positive CTPA would not have PE, yet would be treated. Therefore,
the probability of harm without benefit in treating after a positive CTPA would be lower than treating with a p[PE] of 0.014 (Alternative
1). Treatment would seem safer. Another consideration: with a negative CTPA, the post- test probability would be 0.003, well below p*
and a clear indication for no treatment. With a pre- test p[PE] of 0.014, the probability of a negative CTPA would be 0.95.
Alternative 3: Observe the patient after a negative D- dimer. This would eliminate any risk of hemorrhage but would fail to treat
1.4 patients per 100with PE, leaving them at an unknown risk of death from untreated PE.
This discussion illustrates some of the considerations in decision making. Other factors are statistical uncertainty in
point estimates of probabilities derived from measurements of SE and SP and the output of clinical prediction rules.
CTPA SE and SP may differ according to the results of other tests and patient factors (as discussed in Chapter5). Long-
term cancer risk from radiation exposure, not represented in the decision model in Section13.3.4, would be a concern
in younger patients who would face many years of living with a small increase in the risk of cancer.
Low Wells Criteria Score and D- dimer positive: With a low Wells Criteria score (p[PE]=0.11), the post- test probability
of PE after a positive D- dimer is 0.17, which is within the Test range for the CTPA. If the CTPA was positive, the p[PE]
would be 0.81, well above pU and a clear indication to treat. If the CTPA was negative, the p[PE] would be 0.035, well
Table 13.7 The probability of PE with the Wells Criteria score 1 or zero (p[PE]=0.11) and corresponding D- dimer and CTPA results.
D- dimer result after low
Wells Criteria score p[PE] after D- dimer result p[PE] if CTPA positive p[PE] if CTPA negative
Positive p=
0.17 0.81 0.035
Negative p= 0.014 0.23 0.003
0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
1.0
pL
pU
p*
Treat
No treat
Test range for CTPA
p[PE]
Probability of pulmonary embolism
T+
Wells
criteria
score ≤1,
D-dimer
negative
Figure 13.13 Deciding about doing a CTPA. With a low Wells Criteria score and a negative D- dimer, the p[PE] is 0.014, just above pL for the
CTPA(0.011). A positive CTPA would raise p[PE] to 0.23, which is above p*. Starting treatment would maximize the patient’s expected utility.
T+represents a positive test for D- dimer.
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296 Medical decision making
below p* and an indication to withhold treatment. Doing a CTPA after a positive D- dimer would give a clear answer
regardless of the result of the CTPA.
Wells Criteria score of≥2 The pre- test p[PE] is 0.37, within the Test range for the D- dimer test (0.115–0.66). Therefore,
a D-
dimer is indicated. p[PE] after a positive D- dimer (T+) would be 0.50 (Table 13.8). After a negative D- dimer (T−),
p[PE] would be 0.06. Both probabilities are within the Test range for CTPA (0.011–0.55). Since p[PE] is within the Test
zone for CTPA regardless of the D- dimer result, the D- dimer result does not help decide whether to do a CTPA. Thus,
it would be
logical to proceed directly to a CTPA if the Wells Criteria score was 2 or greater. Figure13.14 shows the
situation graphically.
The example of decision making for suspected PE shows the power of the treatment threshold model. It provides a
transparent, evidence-
based approach to the sequence of a testing decision followed by a treatment decision. It shows
how to maximize your patient’s expected utility by following the guidance of the testing and treatment threshold prob-
abilities. When test results become known, using the guidance of the treatment threshold probability about whether to
treat will maximize your patient’s expected utility. Said differently, when uncertain about what to do, choose the
option that will maximize the patient’s expected utility.
13.6 Accounting forthe non- diagnostic effects ofundergoing atest
From this book’s perspective, the role of a diagnostic test is to change the probability of the target condition. Tests do
have adverse effects, and they could outweigh the benefit of testing. In principle, given a large-
enough utility loss from
undergoing a test, the patient would be better off deciding between Treat and No Treat without undergoing the test.
Tests often cause the patient some discomfort, and some can cause very unpleasant adverse effects. Claustrophobia-
prone patients can become very anxious undergoing an MRI. Doing a test can delay the start of treatment when the test
result is needed to decide whether to treat. Tests cost money. Are these effects of testing bad enough to forgo an other-
wise indicated test? In the framework of this chapter, will the adverse effects shrink the testing zone to the point where
the patient’s probability is no longer within the Test zone defined by pL and pU?
The adverse effects of testing mean that using a test to reach a treatment decision usually decreases the patient’s util-
ity for the resulting outcome. In principle, even sitting in the waiting room prior to a test reduces one’s utility. The
exception: when the patient asks for a test to reassure themselves.
Consider two scenarios. In the first scenario, the patient has the targeted medical condition (D+) and the treatment
is started (A+) without doing the tests. (Notation: in this section A+ has the same meaning as A+ elsewhere in this
chapter). The patient’s outcome utility for this scenario is U(D + A + Notest). The second scenario is exactly like the first
except that the test result is used to make the treatment decision. The patient’s outcome utility is U(D + A + Test).
Stating that testing usually decreases the patient’s utility implies the following:
No test Test
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
Test range for CTPA
p[PE]
Probability of pulmonary embolism
T+T–
Figure 13.14 Testing for D- dimer with a high Wells Criteria score. The p[PE] when the Wells Criteria is ≥2 is 0.37, within the Test zone for D- dimer.
The post- test p[PE] after a negative D- dimer is 0.06 and 0.50 after a positive D- dimer, both within the Test zone for CTPA (0.011–0.55).
Table 13.8 Post- test p[PE] with the Wells Criteria score ≥2 (p[PE]=0.37) and D- dimer and CTPA results.
D- dimer result after high
Wells Criteria score (≥2)
p[PE] after
D- dimer
p[PE] if CTPA is positive
after D- dimer result
p[PE] if CTPA is negative
after D- dimer result
Positive p=
0.50 0.95 0.15
Negative p= 0.06 0.57 0.01
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Selection andinterpretation ofdiagnostic tests 297
Therefore, let Δ denote the amount that testing reduces the patient’s utility for this outcome. That is
UD AUDANo test Test
Note that since testing usually reduces the patient’s utility for an outcome, Δ is usually a positive number.
So far, we have only discussed the utility loss from testing when the patient has the disease and receives treatment.
We denote this state by the pair D+A+. What about the other possible combinations of the disease state (D+ and D−)
and treatment (A+ and A−)?
In general, the amount that testing reduces the patient’s utility will depend on the patient’s actual disease state and
treatment decision. To simplify the presentation, we assume that the utility reduction is roughly the same for all out-
comes. That is, if Δ is such that
No test Test
then we assume the following approximations:
No test Test
No test Test
No test Test
These approximations will help us see how nondiagnostic effects of testing can affect the testing thresholds PL and PU.
Assuming that the utility loss from testing is roughly the same for the four possible outcome states, the expected
utility for testing is as follows:
pD UD A
pD UD A1SE
pD UD A1SP
pD UD ASP
Figure13.15 uses this equation to show how the patient’s utility with testing varies with the probability of the
disease. Notice in Figure13.15 that the lower testing threshold increases, and the upper testing threshold decreases,
as Δ increases. In other words, an increase in the adverse effects of testing leads to a narrower zone of the disease
probabilities within which testing has the highest expected utility (Figure13.15).
Probability of disease
0.0 0.1 0.2 0.3
pL pL pUpU
0.4 0.5
p*
0.6 0.7 0.8 0.9 1.0
Utility
Treat
No Treat
Test
U (D – A–)
U (D – A+)
U (D – Test)
U (D – Test)–Δ
U (D + A+)
U (D + A–)
U (D + Test)
U (D + Test)–
Δ
Δ
Δ
Figure 13.15 The gray line connecting U(D− Test) and U(D+ Test) represents testing when adverse effects of tests are absent. The solid blue line
connecting U(D− Test)−Δ with U(D+ Test)−Δ represents the utility of testing when adverse effects (signified by Δ) of testing are present. The left
solid vertical gray line indicates the probability of disease at the intersection of the No Treat line and the U(D− test) line. The right solid vertical gray
line indicates the probability of disease at the intersection of the Treat and the U(D− test) lines. The left vertical dashed line represent the probability
of disease at the intersection of the No Treat line and the U(D− Test)−Δ line. The right dashed vertical gray line indicates the probability of disease
at the intersection of the Treat line and the U(D+ Test)−Δ line. The dashed vertical lines are much closer to each other than the solid gray vertical
lines, indicating that taking the harms of treatment into account narrows the range of disease probabilities at which Testing is indicated.
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298 Medical decision making
A constant utility loss from testing changes the expressions used to calculate the testing thresholds. Under the
constant utility loss assumption, the following equations show how the nondiagnostic effects of a test affect the
testing thresholds. In these equations, H is the harm from treatment, and B is the benefit from treatment, as defined
in Section13.3.2.
L
SP
SP SE
p
HB
pp
*
**
1
11
U
SP
SP SE
p
HB
pp
*
**
11
13.7 Sensitivity analysis
Sensitivity analysis tests the stability of the output of a decision model as the model’s parameters vary (see Chapter7
for a full discussion). Consider a decision analysis that compares the expected utility of two actions. One-
way sensitiv-
ity analysis measures the effect of varying one model parameter on the expected utility of the two actions. The analyst
starts by substituting the lowest plausible value for the parameter, recalculates the expected utility of the two actions,
and repeats the process over the full range of plausible values for the parameter. If the expected utility of one of the
actions is always higher than the other action, the parameter is not critical to the decision.
With the threshold model, the main drivers of decision making are:
• SE and SP of the test
• The treatment threshold probability, p*=H/(H+B)
• B=U[D+A+] −U[D+A−)
• H=U[D−A−] −U[D−A+]
• The pre- test probability
• The patient’s utility for a health state that they may experience.
In this section, one illustrative sensitivity analysis addresses an unknown quantity, the mortality rate when a patient
with a PE (D+) does not receive anticoagulation (A−). This quantity is needed to estimate U(D+A−) and thus the benefit
of treating PE, which is U(D+A+)
−U(D+A−). As noted earlier, the only published studies date from the 1950s, when
the reported mortality rate was approximately 30%. The current mortality rate of untreated PE is unknown but prob-
ably much lower. The author set the mortality of untreated PE at 5% in the decision tree to calculate p* (Figure13.4).
The sensitivity analysis models p* for several hypothesized mortality rates for untreated PE, ranging from 3.2% to 32%.
Figure13.16 shows that p* increases sharply as the mortality of untreated PE, falls below 5%. This result is consistent
with the following reasoning: as the mortality without treatment approaches the mortality with treatment, the value of
treatment declines, and one should require more diagnostic certainty before treating with potentially lethal drugs.
0.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
0.3500
0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000
0.3500
Treatment threshold probability (p*)
Hypothetical probabilityofdeath from untreated PE
Effect of the mortality rate of untreated PE on
the treatment threshold probability.
Figure 13.16 Treatment threshold probability for PE calculated for different probabilities of death from untreated PE.
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Selection andinterpretation ofdiagnostic tests 299
A second sensitivity analysis (Table13.9) uses the decision model depicted in Figure13.5 to calculate p* for different
probabilities of intracranial hemorrhage while taking anticoagulation to treat a PE. A lower probability of hemorrhage,
which implies safer treatment, lowers p*, widening the range of probabilities at which treatment has the highest
expected utility.
Table 13.9 Effect ofthe probability ofintracranial hemorrhage onthe treatment threshold probability.
Probability of intracranial hemorrhage Treatment threshold probability
0.002 0.036
0.004 0.072
0.006 0.108
0.008 0.146
0.01 0.181
0.015 0.271
0.02 0.451
Table 13.10 Effect ofutility forsevere intracranial hemorrhage onthe treatment threshold probability.
Utility of severe stroke after intracranial hemorrhage Treatment threshold probability, p*
0 0.201
0.2 0.184
0.4 0.167
0.6 0.151
0.8 0.134
1.0 0.118
Table 13.11 Effect ofutility forsevere intracranial hemorrhage onthe width ofthe Test zone.
p[ICH]
No treat- test threshold
probability (pL) for D- dimer
Test- Treat threshold
probability (pU) for D- dimer
Width of Test
zone (pU−pL)
0 0 1.0
0.002 0.022 0.248 0.226
0.004 0.044 0.407 0.363
0.006 0.067 0.517 0.450
0.008 0.108 0.601 0.493
0.010 0.115 0.760 0.545
0.015 0.180 0.832 0.586
0.020 0.250 0.912 0.582
ICH=intracranial hemorrhage.
A third sensitivity analysis (Table13.10) describes the effect of varying the utility for severe stroke after an intracra-
nial hemorrhage. The baseline utility is very low, 0.2419 on a scale of 0–1.0, implying a low value placed on very poor
quality of life. In the sensitivity analysis, as the utility for severe stroke is increased up to 1.0 (perfect health), p* goes
down, enlarging slightly the range of p[PE] at which treatment should be preferred. This effect suggests that with fewer
concerns about the state of health after a severe stroke due to bleeding, a person would want more opportunity for
treatment with anticoagulation, which implies treatment at a lower probability of PE.
A final sensitivity analysis (Table 13.11) explores the relationship between the incidence of treatment- related intrac-
ranial hemorrhage (ICH) and the testing threshold probabilities pL and pU. Here, a rising incidence of ICH is associ-
ated with a convex-
upward rising curve for the width of the Test zone. The result seems to imply that a clinician should
be more willing to test for PE when the patient has an increased risk of a catastrophic cerebral hemorrhage.
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300 Medical decision making
13.8 Decision curve analysis
Decision Curve Analysis (DCA) addresses the same problem as the expected utility treatment threshold model of deci-
sion making described in this chapter: “given this patient’s findings, do I treat, get more information, or do neither?”
With the expected utility threshold model, the patient’s probability of the target condition determines which of these
options should be preferred. With the DCA approach, the clinician’s subjective threshold probability for treating the
target condition determines the preferred option.
The expected utility treatment threshold model may require assessing the patient’s utilities for the outcomes they
may experience, depending on their effect on the treatment threshold probability (p*) in a sensitivity analysis (see
Table13.10 in the preceding section). Clinicians probe the patient’s concerns about possible treatment, but they seldom,
if ever, assess a patient’s utilities by the methods described in this book. Vickers and Elkin, the developers of DCA,
describe a method that uses the clinician’s subjective treatment threshold probability, which might serve as a proxy for
the patient’s utilities, to decide whether to treat, get more information, or do neither.
The product of DCA is a plot of net benefit (y-
axis) vs. the clinician’s p* (x- axis) for the individual patient, as
shown in Figure13.15 (Notation: p* has the same meaning here as elsewhere in this chapter: the probability at which
the decision maker is indifferent between treating and not treating). The clinician chooses to do nothing, get more
information, or treat everyone, depending on which option has the largest net benefit at the clinician’s estimate of
p* (Figure13.17).
DCA defines net benefit as follows:
Net benefit=(proportion of positive test results that are true-
positives in the total population)–(proportion of posi-
tive test results that are false- positives in the total population) × (p*/(1−p*)).
DCA weighs the potential harms of a false- positive test result by (p*/(1−p*), where p* is equivalent to the Harms of
treatment divided by Harms + Benefits of treatment. The larger the ratio of harms to benefits, the larger the weight and,
by the definition of Net Benefit, the lower the Net Benefit.
Net
Benefit
Treatment threshold probability (p*)
0
Test
Treat all
Treat no one
Figure 13.17 A hypothetical decision curve. The horizontal line represents treating no one. The slanting straight line represents treating everyone.
The curve represents getting more information, such as a diagnostic test or using a clinical prediction model.
13.8.1 Making the plot of net benefit vs. p*
The task of making the plot of net benefit (y- axis) vs. the clinician’s p* (x- axis) will fall to a researcher who has access
to a data set of many patients suspected of having a disease. The record for each patient in the data set contains the
clinical predictors of p[D] for the prediction model or the results of the diagnostic test being assessed. The end point is
a plot of net benefit (vertical axis) vs. the clinician’s treatment threshold probability (p*, horizontal axis) for (1) treat no
one; (2) use the clinical prediction model or diagnostic test, or (3) treat everyone. A clinician could use this plot to
decide between these options at the clinician’s treatment threshold probability (Figure13.17).
The process of making the plot assumes that every person in the data set is treated. The DCA definition of a TP and
FP test result refers to whether the patient was treated correctly. The definition of “treated correctly” is a probability
above the clinician’s p* as determined by the clinical prediction model or test result. “Treated incorrectly” is defined as
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Selection andinterpretation ofdiagnostic tests 301
a probability below the clinician’s p*. The role of the clinical prediction model or diagnostic test result is to estimate the
patient’s posterior probability.
• True-positive result: The patient’s posterior p[D] exceeds p*. Therefore, the patient would have been treated
correctly.
• False- positive result: The patient’s posterior p[D] is below p*. Therefore, the patient would have been treated
incorrectly.
To summarize, the product of DCA is a plot of net benefit (y- axis) vs. the clinician’s p* for the individual patient
(x-
axis). The goal of the analysis is a value of net benefit across all patients in the data set for each value of p* within
a clinically plausible range. For each value of p*, the process generates a count of true-
positive and false- positive
results and uses that to calculate the proportion of results that are true-
positive or false- positive across all patients in
the data set.
To generate a plot of the Net Benefit of getting more information vs. p* proceed as follows:
1. Set p* equal to the lowest plausible value, say 0.05.
2. For each patient in the data set, determine if the probability of the target condition, from the prediction model or
post-
test probability, is above or below p* = 0.05 and classify the result as a true- positive or a false- positive,
respectively.
3. Using as the denominator all patients in the data set, calculate the proportion with a true- positive result and the
proportion with a false-
positive result.
4. Use the DCA Net Benefit formula to calculate net benefit as a point on the y- axis corresponding to p*= 0.05 on the
x-
axis.
5. Using the data set, repeat steps 2–4 for every value of p* from 0.05 to a higher but plausible number, perhaps
0.50.
6. Plot the Net Benefit of getting more information (y- axis) vs. p* (x- axis).
The Decision Curve Analysis approach compares the net benefits of (1) getting more information, as described
earlier; (2) assuming that no one has the target condition and therefore does not receive treatment for any value of p*;
(3) assuming that everyone has the target condition and is treated for all values of p*.
Net benefit of treating no one: Assume that no patients receive treatment regardless of their probability of the target
condition. The DCA defines a true-
positive (the patient’s probability is >p* and treatment is given), and a false- positive
(the patient’s probability is <p* and treatment is given). If no one is treated, no one has a true- positive or false- positive
result. Therefore, the Net Benefit of testing will be zero at all values of p*, which is represented on the plot of Net
Benefit vs. p* by a horizontal line intersecting the y- axis at Net Benefit=0.
Net benefit of treating everyone: Assume that all patients would be treated (“treat all”), regardless of their probability
of the target condition. Using the DCA definitions of true-
positive and false- positive, p* is the cut- point to define
whether a positive test is a TP or an FP result. As p* increases, the proportion of all positive test results that are above
p* decreases, which means that the proportion of positive results that are true- positive results decreases and, corre-
spondingly, the proportion that are false- positive results increases. Remembering the formula for Net Benefit, as p*
increases, the first term (true positives) decreases while the second term (false positives) increases. The overall result is
a decrease in Net Benefit as p* increases.
13.8.2 Use of DCA in practice
1. The clinician must become adept at choosing a p* that fits the clinical context and the patient’s preferences. How
do clinicians choose an appropriate p*? Ideally, they know the harms and benefits of the proposed treatment and
adjust them to fit the individual patient. They can use the heuristics for setting a treatment threshold probability
as described in Section13.3.4.
2. The forgoing advice is aspirational. In this writing, little is known about whether clinicians try to characterize their
treatment threshold probability as a number, letalone how well those numbers match up with a gold- standard
treatment threshold probability.
Summary
DCA has attracted considerable interest. It is the first new approach to using decision analysis in clinical care in many
decades. Its value is to bypass the decision modeling– and the utility assessment– required to estimate p*.
Both expected utility treatment threshold models and DCA share one characteristic: neither, to the author’s knowl-
edge, have been incorporated into day- to- day patient care at scale. The opportunities for research are endless.
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302 Medical decision making
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Dimer for the exclusion of acute venous thrombosis and pulmonary embolism: a systematic
review. Annals of Internal Medicine, 140, 589–602.
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This article describes a now widely used method for relating the net benefit of using a prediction model or a test to a clinician’s subjective
treatment threshold probability.
Summary
1. The topic of this chapter is deciding if a test result could make a difference. If the result could make a differ-
ence, the clinician should order the test.
2. The clinical principle behind the threshold model is: “Do a test only if the results could change your mind
about the next step.”
3. Starting treatment when the diagnosis is uncertain means treating some who do not have the target condition
and may suffer harm– and no benefit– from treatment.
4. As the probability of the target condition changes, so does the relative likelihood of benefit or harm from
treatment which, in turn, drives the need for greater diagnostic certainty.
5. The treatment threshold probability is the probability of the target condition at which one should be indifferent
between giving and withholding treatment.
6. The treatment threshold probability p* is determined by the following ratio:
p
H
HB
*
where H is the net harm from treatment and B is the net benefit from treatment.
7. Two testing thresholds divide the probability scale into three zones: No Treat, Test, and Treat. The testing
thresholds are determined by the treatment threshold probability and the sensitivity and specificity of the test.
8. The harms of a test narrow the range of probabilities within which testing should be preferred.
9. A 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.
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Medical Decision Making, Third Edition. Harold C. Sox, Michael C. Higgins, Douglas K. Owens, and Gillian Sanders Schmidler.
© 2024 John Wiley & Sons Ltd. Published 2024 by John Wiley & Sons Ltd.
303
CHAPTER14
Medical decision analysis inpractice:
advanced methods
The reader may be wondering how the principles in this book have been applied in the real world. The framework for
this chapter is three example analyses. The first of these has informed policy for screening for HIV, the second has
informed clinical evaluation and management in lung cancer, and the third has demonstrated the cost‐
effectiveness of
a promising new therapy. One of the most important examples in current practice is the systematic use of decision
analysis to inform the cancer‐ screening recommendations of the US Preventive Services Task Force (USPSTF) (see
Barry etal.,2023; Owens etal.,2016; Petitti etal.,2018). The USPSTF recommendations for screening for lung cancer,
colorectal cancer, breast cancer, and cervical cancer all are based in part on sophisticated models developed by the
Cancer Intervention and Surveillance Modeling Network (see for example, Knudsen etal.,2021). In each of these cases,
decision analysis has informed guidelines for practice that clinicians implement without being aware that decision
analysis has shaped the actions they take in their daily work. A remaining goal, as yet out of reach, is to inform deci-
sions custom‐ tailored to the clinical characteristics and preferences of an individual. The last section of this chapter
touches upon this topic.
The purpose of this chapter is to show the reader how the concepts covered in the book are used in real‐ world analy-
ses that shape daily practice. These real‐ world analyses are much more complex than the examples used in previous
chapters, but the underlying concepts are the same. The models we discuss here have been published in leading medi-
cal journals, and each required over a year of full‐
time effort to develop.
14.1 An overview ofadvanced modeling techniques
Many of the real‐ world problems that people analyze are quite complex. In this book, we showed how to use decision
trees to represent a decision problem. Analysts typically use a decision tree to represent problems in which all the
events occur either immediately or within a short time frame (as shown in Chapter6). If events may occur at different
points in time, decision trees may become very large and difficult to understand. In general, for clinical problems in
which events occur over long time horizons (e.g., cancer), events occur repeatedly, or one group interacts with another,
the decision tree representation usually is not sufficient. We will discuss briefly several advanced modeling methods
that can represent such events faithfully (also see Chapter12 on Markov models). The publications at the end of the
chapter provide more detailed explanations of these methods.
14.1
An overview ofadvanced modeling techniques 303
14.2
Use of medical decision‐ making concepts to analyze a policy problem:
the cost‐
effectiveness of screening for HIV 305
14.3
Use ofmedical decision‐ making concepts toanalyze aclinical diagnostic problem:
strategies todiagnose tumors inthe lung
313
14.4
Calibration andvalidation ofdecision models 317
14.5
Use ofcomplex models forindividual‐ patient decision making 319
Bibliography 321
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304 Medical decision making
14.1.1 When are advanced modeling approaches needed?
The decision about when to use more advanced methods depends on the decision problem. Modeling approaches
other than decision trees are usually needed when the clinical problem:
• Requires representing the natural history of a chronic disease (e.g., cancer);
• Has events that occur over long time horizons (e.g., heart disease);
• Has events that can occur multiple times (e.g., opportunistic infections in people living with HIV);
• Requires representing the transmission of an infectious disease (e.g., HIV, tuberculosis, and influenza);
• Involves interactions among groups (e.g., patients and clinicians in a model that addressed how to treat patients
more efficiently);
• Involves resource constraints (e.g., a limited number of hospital beds in a model that addressed how to triage
patients in an influenza pandemic).
Each of these situations would be difficult to represent in a decision tree. For complex problems with long time hori-
zons, the decision tree would become too large. For problems that require modeling interactions between groups over
time, the decision tree is not suitable because it cannot depict such interactions.
14.1.2 Types ofmodeling approaches
A variety of modeling frameworks are suitable for representing complex medical decision problems. All of the
approaches described here use computer‐
based mathematical simulations. The analysts can implement these models
in software developed specifically for the modeling approach, in more general programming software, and for some
of the approaches, in spreadsheet software.
The most common type of model used currently for medical decision problems is the state‐
transition model (see
Siebert etal.,2012). This general term describes several modeling approaches that we will define and explain briefly.
Interested readers should read the publications at the end of the chapter for more detail and guidance on how to
develop these models.
State‐
transition models characterize the health states of a disease (e.g., HIV) or of an epidemic (e.g., the at‐ risk
population) as a sequence of transitions from one state of nature (or health state) to another. For example, a health
state‐ transition model of the natural history of HIV infection in a given individual might define health states in terms
of CD4lymphocyte counts or HIV‐ RNA levels. Analysts can use state‐ transition models to estimate the changes in
length and quality of life and costs for a cohort of persons who undergo a particular intervention, either preventive or
therapeutic. These models allow for a running tally of all clinical events, the length of time spent in each health state,
and the costs and quality of life associated with each health state. These, in turn, make it possible to compute overall
health and economic outcomes such as average life expectancy, quality‐
adjusted life expectancy, cost, and
cost‐ effectiveness.
There are several types of state‐ transition models. Markov models, introduced in Chapter12, are a special class
of state‐ transition models. They are relatively easy to specify and are used widely. The Markov assumption specifies
that the probability of transition to another state depends only on the current health state. Because past history is
often important in clinical problems, the Markov health states must be specified with care to avoid violations of the
Markov assumption. For example, the probability of recurrence of breast cancer may depend on how many years
have elapsed since treatment. To represent this clinical history in a Markov model therefore often requires expand-
ing the number ofhealth states. A breast cancer model might need to include a state for each year after initial treat-
ment (e.g., year 1, year 2, ..., year 20). Markov models are very useful, but if the relevant clinical history is very
complex, the models may require so many health states that they become difficult to develop, debug, and
understand.
In such situations, another approach is to use a generalized health state‐ transition model, often called an “individual‐
level state‐ transition model,” or microsimulation model. These models provide a means of flexibly modeling events
over time when a Markov model would have too many states to be tractable. In a microsimulation model, the model
comprises specific individuals that have particular attributes (such as age and gender) and can have a complex history
(such as a history of a disease, associated treatment, and complications). As time progresses in the model, the history
of each person can develop as events occur (e.g., a stroke) with specified probabilities. The approach allows for
complex health states, but the model must track the trajectory of each of many individuals (usually thousands or more).
So,this approach is often more computationally intensive than are Markov models. For example, see the paper by
Bendavid etal. (2008) in the list of references at the end of the chapter.
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