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Contents ix
12 Markov models, 248
12.1
Introduction, 248
12.2
Markov model basics, 249
12.3
Determining transition probabilities, 259
12.4
Markov model analysis– anoverview, 269
Epilogue, 277
Bibliography, 277
13 Selection andinterpretation ofdiagnostic tests, 278
13.1
Introduction, 278
13.2
Four principles ofdecision making, 279
13.3
The threshold probability fortreatment, 281
13.4
Threshold probabilities fortesting, 288
13.5
Clinical application ofthe threshold model ofdecision making, 293
13.6
Accounting forthe non- diagnostic effects ofundergoing atest, 296
13.7
Sensitivity analysis, 298
13.8
Decision curve analysis, 300
Bibliography, 302
14 Medical decision analysis inpractice: advanced methods, 303
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
screeningforHIV, 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
15 Cost- effectiveness analysis, 323
15.1 The clinician’s conflicting roles: patient advocate, member ofsociety, andentrepreneur, 323
15.2 Cost- effectiveness analysis: amethod forcomparing management strategies, 325
15.3 Cost–benefit analysis: amethod formeasuring thenet benefit ofmedical services, 330
15.4 Methodological best practices forcost- effectiveness analysis, 332
15.5 Reference case forcost- effectiveness analysis, 333
15.6
Impact inventory forcataloguing consequences, 334
15.7 Measuring thehealth effects ofmedical care, 334
15.8 Measuring thecosts ofmedical care, 335
15.9 Interpretation ofcost- effectiveness analysis anduse indecision making, 337
15.10 Limitations ofcost- effectiveness analyses, 337
Bibliography, 338
Index, 340
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xi
Foreword
The diagnostic tools available to today’s clinicians are breathtaking. Scans explore previously inaccessible life-
threatening disorders and space- occupying lesions. Scopes invade nearly every tubular structure, finding tumors and
inflammatory diseases. Panels of antigen tests identify a panoply of microscopic invaders. PCRs and genome
sequencers seek out the rarest of the rare. Given the accuracy provided by scanning, our thin biopsy needles and our
drainage catheters can be safely inserted; even our invasive procedures are less invasive and less risky. Biopsying the
pancreas or the heart is no longer science fiction.
These technical advances are dramatically altering our time- honored approach to diagnosis. Whereas we previously
delved deeply into a patient’s illness history and meticulously carried out a physical examination looking for salient
clues to guide our next diagnostic or therapeutic recommendation, now, bolstered with merely a chief complaint or a
cursory examination, clinicians scan the chest, or abdomen, or head (or all three); send for panels of tests; and wait for
the results for further guidance. To old-
time doctors, this process feels like a violation, yet it often yields answers more
efficiently, achieves earlier treatment, and reduces hospital stays.
The new era in diagnostic expertise ushered in by technical innovations should be satisfying to the profession and
the public, but it has not been. Within the profession, we battle over how to use prostate-
specific antigen (PSA) and
bone density tests; we argue whether prediabetes and long COVID really exist. We offer conflicting advice to the public
on when to get a colonoscopy or when to wear masks. We confuse our trainees by repurposing diagnostic criteria from
controlled trials into clinical entities and by using lists of numerical diagnostic summations, as if a single calculated
number is meaningful. But we fail even more fundamentally when we make diagnostic mistakes that cost patients not
just their peace of mind but their lives. Outcomes researchers tell us that thousands of costly medical errors occur
everyyear and that many are attributable to faulty diagnosis. The problem of errors became so acute several years ago
thatexpert panels convened by the National Academy of Medicine issued reports highly critical of existing medical
practices.
Therapeutics have shared scientific progress in diagnosis. New diseases have appeared, some diseases have been
reclassified based on new pathophysiologic understanding, transplants are commonplace, and a substantial fraction of
the population became immunosuppressed for one reason or another. A pharmacopeia of new powerful drugs came
into wide use, replete with its vast benefits and its inevitably troublesome risks and costs. Practice also evolved. Over
the years, the choice of one treatment or another was based primarily on individual doctors’ experiences and personal
preferences or the opinion of experts. For better or worse, the profession did recognize that this chaotic method had to
be replaced by greater standardization, itself based on available rigorous clinical research. Data from research studies
today are combined, analyzed, and packaged for everyday use. The choice of alternative treatment regimens has been
rigorously subjected to probabilistic reasoning and decision science, thus illuminating the basic principles of therapy.
The public also became engaged. Diagnosis and therapeutics are no longer the exclusive purview of professionals;
they are the talk of the town. Access to case reports in the Sunday newspapers, clinical image entries on social media,
talking stool-
testing boxes on television, and endless, often authoritative, data on easily accessible search engines have
helped make the public our partners in all things medical. And for that, we should be grateful.
Needless to say, medical researchers have not been inattentive to the persistence of medical diagnostic and therapeu-
tic errors. During most of the twentieth century, only a few lone voices were offering new ideas, but during the past
five decades, clinical decision- making has been a prime focus, particularly in divisions of General Internal Medicine in
Departments of Medicine. Investigators have clarified the language and stages of the diagnostic process, illuminated
causal reasoning, defined the inextricable association between testing on one hand and the risks and benefits of treat-
ment on the other, clarified the role of probabilistic thinking, applied mathematical formulations to decision- making,
and pressed physicians on the merits of making all judgments on a hierarchy of solid data. Professional societies have
embraced diagnostic sections in their national meetings, several major journals feature an array of medical images, and
medical schools have introduced clinical reasoning courses.
Diagnosis and therapy selection are physicians’ fundamental tasks, principal skills, and awesome responsibility.
Many believed that by now, artificial intelligence or machine learning would take over medical diagnosis and therapy.
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xii Foreword
Regrettably, waiting for this transition is like waiting for Godot: it hasn’t happened and it won’t happen soon: we’re
still on our own.
Many of the concepts and language in Medical Decision Making have already seeped into day- to- day medical practice.
Decisions on which scan to use for suspected pulmonary embolism are couched in probabilities, likelihood ratios, false
positives, and false negatives. Terms such as Bayes’ Rule, decision analysis, utility theory, and decisional toss-
ups,
though uncommon, are used by clinicians as rationales for clinical decision-
making. Slow seeping is fine, but it is not
sufficient.
Fortunately, the basic principles and practices of clinical diagnostics and therapeutics have come a long way, and
they are superbly described in Medical Decision Making. This new edition contains much new and advanced material:
decision models, clinical prediction models, survival analysis, patients’ utility assessment, the threshold approach to
testing and treating, and cost- effectiveness analysis, to name only a few. In many ways, the breadth and extent of these
approaches represent a mathematics of medical thinking. The third edition of Medical Decision Making will be the refer-
ence standard of the field for decades.
For physicians eager to improve their abilities, for teachers of clinical medicine, and for medical students trying to
comprehend the basic concepts of clinical reasoning and decision-
making, Medical Decision Making is the “go- to” book.
Becoming comfortable with the concepts in the book will require concentration, discipline, and persistence, but the
effort will be well worth it.
Jerome P. Kassirer, M.D.
Distinguished Professor, Tufts University School of Medicine
Editor- in- Chief Emeritus, New England Journal of Medicine
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xiii
Preface
The textbook Medical Decision Making (MDM) took form in the mid- 1980s as an extension of the notes for an introduc-
tory course for medical students. The notes and slides became the draft of a book. The draft found a publisher and,
eventually, readers from everywhere. Thanks to leaders like Barbara McNeil, Ron Howard, Stephen Pauker, Jerome
Kassirer, Amos Tversky, and Daniel Kahneman, the foundations of decision science were in place at the time of the first
edition. But the field has continued to grow, and a standard textbook must keep pace with change.
The ultimate measure of the field of medical decision making is its effect on medical education, decision making in
clinical practice, and clinical policies.
In education, Bayes’ theorem is a gift to clinical teachers, especially in its odds ratio form. Think of a patient with high pre- test odds
of a clinical condition and a negative result on a test with low sensitivity. The students are stunned by how little the odds change.
Ateachable moment.
Do clinicians use decision analysis in day-
to- day care? I suspect that opportunities are infrequent, given the high- pressure condi-
tions of office practice. When they do arise, clinicians need quick access to the evidence. Posting a list of frequently used tests and
their likelihood ratios on the wall of each examination room would be one way to address that need. More complicated decision making
would require a smartphone app built around a decision model like the one for pulmonary embolism in Chapter13.
Practice guidelines do affect the world of office practice, and some guidelines were shaped by advanced decision models like those
described in Chapter14. The US Preventive Services Task Force relies on sophisticated decision models to inform their cancer screen-
ing recommendations.
This volume addresses these needs. Chapters1 and2 set the stage: uncertainty is everywhere in clinical practice, yet
clinical reasoning depends on logical deduction as exemplified by differential diagnosis. Chapters3,4, and5 are about
defining and navigating uncertainty: determining probability, updating probability, and the determinants of post-
test
probability, all basic tools of the clinician. Chapters 6 and7 are about modeling the factors that shape decisions.
Chapters8–12 explore in- depth the measurement of utility, both the basics and the underlying theory. Topics include
attitudes toward taking risks, the quality of life, and the length of life. The last three chapters are about making deci-
sions: deciding when to treat, when to test, and when to wait (Chapter13); the advanced modeling methods that
inform policy (Chapter14); and cost-
effectiveness analysis (Chapter15).
This book describes how to translate subjective judgements about events into numbers—probabilities and utilities—
with which to identify the best decision—treat, test, or do nothing—for an individual. While the book uses a numerical
framework to guide decision making, the actual math is straightforward except for parts of Chapters 8–12. Even there,
the text surrounding the math will explain the basic concepts. Bottom line: when the reader finds the math
challenging,
read on. The text will explain what it means.
A brief update on the authors: Mike Higgins teaches a high-
level course on medical decision analysis for Stanford
University graduate students and medical students. The middle chapters are an outgrowth of his lectures. Doug
Owens has continued to do advanced decision modeling to inform clinical policy making while adding several aca-
demic leadership responsibilities to his portfolio at Stanford. We welcome Gillian Schmidler, PhD, as a co- author. She
is a member of the faculty at Duke University. She co-
led the Second Panel on Cost- Effectiveness, a group of experts
that has literally set the standards for study in that field. Chapter15 is an outgrowth of her work with the Panel.
Iretired recently after 9 years developing a peer review program for the Patient- Centered Outcomes Research Institute
(PCORI), an organization that funds clinical comparative effectiveness research.
A word about artificial intelligence and the contents of this book: In the past year, advances in machine learning
analysis of very large observational data sets has raised the possibility that clinical reasoning could evolve toward a
model in which clinician and machine collaborate. This possibility raises questions. How will observations based on
machine learning and artificial intelligence interface with clinical reasoning based on good science such as that
described in this book? Will clinical outcomes reflect decisions that incorporates the preferences of a specific patient for
potential downstream health states? In a vast observational data set, the patient characteristics, treatments, and out-
come as well as the relationships between them are all subject to the biases described in this book and elsewhere.
While the way forward is uncertain, readers of this book should be well-placed to evaluate AI-based input against a
reference standard based upon scientific observation and reasoning.
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xiv Preface
We thank the following individuals who read chapters at our request and gave us good advice, both clinical and
technical: John Wong, Ross Schacter, and Marc Dewey. Many thanks also to Jerome P. Kassirer, internist, editor, and
pioneer in our field whose Introduction sets the stage for the third edition of MDM and to Jeremy Goldhaber-Fiebert
for advice about medical decision analysis in the age of artificial intelligence.
We hope that this book achieves two goals. The first is to introduce readers to basic concepts that may enrich their
lives in the practice of medicine or their experiences as a patient. The second is to attract leaders– present and future–
who will take these ideas into their field– medicine, policy making, and research– and advance it to the next level.
We’ll be watching!
H.C.S.
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1
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.
CHAPTER1
Introduction
“Proof,” I said, “is always a relative thing. It’s an overwhelming balance of probabilities. And that’s a matter of how they strikeyou.”
(Raymond Chandler in Farewell, My Lovely, 1940)
Thoughtful clinicians ask themselves many difficult questions during the course of taking care of patients. Some of
these questions are as follows:
• How may I be thorough yet efficient when considering the possible causes of my patient’s problem?
• How do I characterize the information I have gathered during the medical interview and physical examination?
• How should I interpret new diagnostic information?
• How do I select the appropriate diagnostic test?
• How do I choose among several risky treatments?
The goal of this book is to help clinicians answer these important questions.
The first question is addressed with observations from expert clinicians “thinking out loud” as they work their way
through a clinical problem. The last four are addressed from the perspective of medical decision analysis, a quantita-
tive approach to medical decision making.
The goal of this introductory chapter is to preview the contents of the book by sketching out preliminary answers to
these five questions.
1.1 How may Ibe thorough yet efficient when considering thepossible causes ofmy
patient’s problems?
Trying to be efficient in thinking about the possible causes of a patient’s problem often conflicts with being thorough.
This conflict has no single solution. However, much may be learned about medical problem-
solving by listening to
expert diagnosticians discuss how they reasoned their way through a case. Because the single most powerful predictor
of skill in diagnosis is exposure to patients, the best advice is “see lots of patients and learn from your mistakes.” How
to be thorough, yet efficient, when thinking about the possible causes of a patient’s problem is the topic of Chapter2.
1.2 How do Icharacterize theinformation Ihave gathered during themedical interview
andphysical examination?
The first step toward understanding how to characterize the information one gathers from the medical interview and
physical examination is to realize that information provided by the patient and by diagnostic tests usually does not
reveal the patient’s true state. A patient’s signs, symptoms, and diagnostic test results are usually representative of
1.1 How may Ibe thorough yet efficient when considering thepossible causes ofmy patient’s problems? 1
1.2
How do Icharacterize theinformation Ihave gathered during themedical interview
andphysical examination?
1
1.3
How do Iinterpret new diagnostic information? 3
1.4
How do Iselect theappropriate diagnostic test? 4
1.5
How do Ichoose among several risky treatment alternatives? 4
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2 Medical decision making
more than one disease. Therefore, distinguishing among the possibilities with absolute certainty is not possible.
A60-
year- old man’s history of chest pain illustrates this point.
Mr. Costin, a 60- year- old bank executive, walks into the emergency room complaining of intermittent substernal chest pain that is
“squeezing” in character. The chest pain is occasionally brought on by exertion but usually occurs without provocation. When it
occurs, the patient lies down for a few minutes, and the pain usually subsides in about 5 minutes. It never lasts more than
10
minutes. Until these episodes of chest pain began 3weeks ago, the patient had been in good health, except for intermittent
problems with heartburn after a heavy meal.
Although there are at least 60 causes of chest pain, Mr. Costin’s medical history narrows down the diagnostic pos-
sibilities considerably. Based on his history, the two most likely causes of Mr. Costin’s chest pain are coronary artery
disease or esophageal disease.
However, the cause of Mr. Costin’s illness is uncertain. This uncertainty is not a shortcoming of the clinician who
gathered the information; rather, it reflects the uncertainty inherent in the information provided by Mr. Costin. Like
most patients, his true disease state is hidden within his body and must be inferred from imperfect external clues.
How do clinicians usually characterize the uncertainty inherent in medical information? Most clinicians use words
such as “probably” or “possibly” to characterize this uncertainty. However, most of these words are imprecise, as seen
as we hear more about Mr. Costin’s story:
The physician who sees Mr. Costin in the emergency room tells Mr. Costin, “I cannot rule out coronary artery disease. The next step
in the diagnostic process is to examine the results of a stress ECG.” She also says, “I cannot rule esophageal disease either. If the stress
ECG is negative, we will work you up for esophageal disease.”
Mr. Costin is very concerned about his condition and seeks a second opinion. The second physician who sees Mr. Costin agrees that
coronary artery disease and esophageal disease are the most likely diagnoses. He tells Mr. Costin, “Coronary artery disease is a likely
diagnosis, but to know for certain we’ll have to see the results of a stress ECG.” Concerning esophageal disease, he says, “We cannot
rule out esophageal disease at this point. If the stress ECG is normal, and you don’t begin to feel better, we’ll work you up for
esophageal disease.”
Mr. Costin feels reassured that both clinicians seem to agree on the possibility of esophageal disease, since both have
said that they cannot rule out esophageal disease. However, Mr. Costin cannot reconcile the different statements con-
cerning the likelihood that he has coronary artery disease. Recall that the first clinician said “coronary artery disease
can’t be ruled out,” whereas the second clinician stated, “coronary artery disease is a likely diagnosis.” Mr.Costin
wants to know the difference between these two different opinions. Mr. Costin explains his confusion to thesecond
clinician and asks him to speak to the first clinician.
The two clinicians confer by telephone. Although they expressed the likelihood of coronary artery disease differently when they talked
with Mr. Costin, it turns out that they had similar ideas about the likelihood that he has coronary artery disease. Both believe that
about one patient out of three with Mr. Costin’s history has coronary artery disease.
From this episode, Mr. Costin learns that clinicians may choose different words to express the same judgment about
the likelihood of an uncertain event.
To Mr. Costin’s surprise, the clinicians have different opinions about the likelihood of esophageal disease, despite the fact that both
described its likelihood with the same phrase, “esophageal disease can’t be ruled out.” The first clinician believes that among patients
with Mr. Costin’s symptoms, only one patient in ten would have esophageal disease. However, the second clinician thinks that as
many as one patient in two would have esophageal disease.
Mr. Costin is chagrined that both clinicians used the same phrase, “can’t be ruled out,” to describe two different
likelihoods. Mr. Costin learns that clinicians commonly use the same words to express different judgments about the
likelihood of an event.
The solution to the confusion that can occur when using words to characterize uncertainty with words is to use a
number: a probability. Probability expresses uncertainty precisely because it is the likelihood that a condition is present
or will occur in the future. When one clinician believes the probability that a patient has coronary artery disease is 1in
10, and the other clinician thinks that it is 1in 2, the two know that they disagree and that they must talk about why
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Introduction 3
their interpretations are so disparate. The precision of numbers to express uncertainty is illustrated graphically by the
scale in Figure1.1. On this scale, uncertain events are expressed with numbers between 0 and 1.
To understand the meaning of probability in medicine, think of it as a fraction. For example, the word “one- third”
means 33 out of a group of 100. In medicine, if a clinician states that the probability that a disease is present is 33%, it
means that the clinician believes that if they see 100 patients with the same findings, 33 of them will have the disease
in question (Figure1.2).
Although probability has a precise mathematical meaning, a probability estimate need not correspond to a physical
reality, such as the prevalence of disease in a defined group of patients. We define probability in medicine as a number
between zero and 1 that expresses a clinician’s opinion about the likelihood of a condition being present or occurring
in the future. The probability of an event a clinician believes is certain to occur is equal to 1. The probability of an event
a clinician believes is certain not to occur is equal to 0.
A probability may apply to the present state of the patient (e.g., that they have coronary artery disease), or it may be
used to express the likelihood that an event will occur in the future (e.g., that they will experience a myocardial infarc-
tion within 1 year).
When should a clinician use probability in the diagnostic process? The first time that probability is useful in the
diagnostic process is when the clinician feels the need to synthesize the medical information in the medical interview
and physical examination into an opinion. At this juncture, the clinician wants to be precise about their uncertainty
because they are poised to make decisions about their patient. They may decide to act as if the patient is not diseased.
They may decide that they need more information and will order a diagnostic test. They may decide that they know
enough to start the patient on a specific treatment. To decide between these options, they do not need to know the
diagnosis. They do need to estimate the probability that the patient has, as in the case of Mr. Costin, coronary artery
disease as the cause of his chest pain.
A clinician arrives at a probability estimate for a disease hypothesis by using their personal experience and the pub-
lished literature. Advice on how to estimate probability is found in Chapter3.
1.3 How do Iinterpret new diagnostic information?
New diagnostic information often does not reveal the patient’s true state, and the best a clinician can do is to estimate
how much the new information has changed their uncertainty about it. This task is difficult if one is describing uncer-
tainty with words. However, if the clinician is expressing uncertainty with probability, they can use Bayes’ theorem to
estimate how much their uncertainty about a patient’s true state should have changed. To use Bayes’ theorem, a
0 1.00.5
Certain not
to occur
Equal chance
of occurring or
not occurring
Certain
to occur
Probability of disease
Figure 1.1 A scale for expressing uncertainty.
0 1.0
0.5
Probability of disease
p[disease]=0.33
Figure 1.2 A clinician can visualize the level of certainty about a disease hypothesis on a probability scale. Thirty- three is marked on this certainty
scale to correspond to a clinician’s initial probability estimate that Mr. Costin had coronary artery disease.
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4 Medical decision making
clinician must estimate the probability of disease before the new information was gathered (the prior probability or pre-
test probability) and know the accuracy of the new diagnostic information. The probability of disease that results from
interpreting new diagnostic information is called the posterior probability (or post-
test probability). These two probabili-
ties are illustrated in Figure1.3.
Chapter4 explains about how to use Bayes’ theorem to estimate the post-
test probability of a disease.
1.4 How do Iselect theappropriate diagnostic test?
Although the selection of a diagnostic test is ostensibly straightforward, the reasoning must take into account several
factors. In the language of medical decision analysis, the selection of diagnostic tests depends on the patient’s feelings
about states of disease and health, the physician’s estimate of the prior probability of disease, and the accuracy of the
diagnostic tests that the physician is trying to choose between.
A logical approach to selecting diagnostic tests depends on three principles:
• Diagnostic tests are imperfect and therefore seldom reveal a patient’s true state with certainty.
• Choose tests whose results could change your mind about what to do for your patient.
• Clinicians often start treatment when they are uncertain about the true state of the patient.
These three principles lead to an important concept: the selection of diagnostic tests depends on the level of certainty
at which a physician is willing to start treatment. This level of certainty is known as the treatment threshold probabil-
ity. How to use the treatment- threshold probability to make decisions is the topic of Chapter9.
A clinician must take two steps to assess the treatment- threshold probability of disease. The first step is to list the
harms and benefits of treatment. The second step is to assess the patient’s feelings about these harms and benefits. A
decision analyst assesses a patient’s attitudes toward the risks and benefits of treatment using a unit of measure called
utility. Measuring a patient’s utilities is covered in Chapter 8.
1.5 How do Ichoose among several risky treatment alternatives?
Choosing among risky treatment alternatives is difficult because the outcome of most treatments is uncertain: some
people respond to treatment but others do not. If the outcome of a treatment is governed by chance, a physician cannot
know in advance which outcome of the treatment will result. Under these circumstances, the best way to achieve a
good outcome is to choose the treatment alternative whose average outcome is best. This concept is called expected
value decision making. Expected value decision making is the topic of Chapters6,7, and10.
0 1.0
0.5
Probability of disease
Prior
probability
Posterior
probability
Bayes’
theorem
Figure 1.3 The pre- test probability and the post- test probability of disease.
Summary
The care of patients is difficult in part because of the uncertainty inherent in the nature of medical information:
tests are imperfect, and treatments have unpredictable consequences. The application of probability, utility, and
expected value decision making provides a framework for making the right decision despite the uncertainty of
medical practice. Medical decision analysis helps clinicians and patients to cope with uncertainty.
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