[IMPROVEDX] IOM report is released - Diagnosis in actual practice

Amos Cahan acahan at US.IBM.COM
Mon Oct 12 00:18:23 UTC 2015


From a practical point of view, even if thresholds could be set, their
usefulness would be questionable if physicians are unable to assess prior
probabilities. In a study we did, physicians presented with a case vignette
describing a patient with chest pain demonstrated subadditivity, meaning
the sum total of the probabilities they assigned  was >100% (the mean was
137%): http://qjmed.oxfordjournals.org/content/96/10/763.long.
In another study (
http://www.jclinepi.com/article/S0895-4356%2805%2900150-2/abstract), we
found marked variability among physicians in their estimates of the
probability for coronary disease in case scenarios. Interestingly, medical
expertise did not associate with improved agreement among physicians.

The threshold approach is very appealing in theory, but the fact it has not
been widely adopted by physicians in the 4 decades since its introduction
may have to do with their reluctance, and probably limited ability, to
formally handle probabilities.

Amos

Amos Cahan, MD
Research scientist, Clinical Informatics
IBM T. J. Watson Research Center
1101 Kitchawan Road, Route 134
Yorktown Heights, NY 10598
1.914.945.2590
acahan at us.ibm.com






From:	"Giuliano, Michael M.D." <MGiuliano at HACKENSACKUMC.ORG>
To:	IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG
Date:	10/11/2015 06:44 PM
Subject:	Re: [IMPROVEDX] [IMPROVEDX] IOM report is released - Diagnosis
            in actual practice



Great point. Just as an illustration of disease to disease threshold, in
Pediatrics when dealing with potential sepsis in a newborn many would use
as low as a probability of only 1% to do an evaluation for sepsis and begin
therapy with antibiotics. This low threshold is a function of limited
availability of tests that  change the post test probability of disease and
the severe consequences of missing the disease. Each  setting will have
these unique factors that make it impossible to generalize a threshold.

Michael Giuliano MD, MHPE, MEd
Director of Neonatology
Hackensack university medical center
Rutgers , NJMS
Newark, NJ

Sent from my iPhone

On Oct 11, 2015, at 3:44 PM, Hamm, Robert M. (HSC) <Robert-Hamm at OUHSC.EDU>
wrote:

      John Brush raises an interesting issue: is there a general threshold
      probability at which one can ignore a possibility, or at which one
      should treat without further attempt to confirm or disconfirm?
      The alternative would be that for each disease (each test, each
      treatment modality), there would be an appropriate threshold
      probability. The theory by which thresholds are produced would say
      that, of course, the threshold is potentially different for each
      disease. The threshold is based on the two utility impacts -- how
      much harm  you experience if you don't treat a person with a disease
      when you could have treated them; and how much harm you experience if
      you treat a person who does not have the disease for which the
      treatment is intended. Those differ for every disease, in principle.

      Perhaps it is an empirical question -- how much variation is there in
      treatment threshold probabilities (or, test treatment probabilities)
      between different diseases. But unless there is evidence that all
      diseases have similar thresholds, I don't see any reason to ask "is
      there a general threshold probability" or "what should the general
      threshold probability be? 20% 10%? 40%?"

      Rob


      Robert M. Hamm, PhD
      Clinical Decision Making Program
      Department of Family and Preventive Medicine
      University of Oklahoma Health Sciences Center
      900 NE 10th Street
      Oklahoma City OK 73104
      405 271 5362 ext 32306       Fax 405 271 2784
      robert-hamm at ouhsc.edu

      From: John Brush [jebrush at ME.COM]
      Sent: Sunday, October 11, 2015 12:56 PM
      To: IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG
      Subject: Re: [IMPROVEDX] [IMPROVEDX] IOM report is released -
      Diagnosis in actual practice

      Mark, can you send a reference to your study on thresholds? As you
      point out, thinking probabilistically about diagnosis raises
      important questions about thresholds and clinical decision rules.
      Here’s something to think about: For clinical research, we have
      conventionally and arbitrarily chosen thresholds of 0.05 and 0.20 for
      alpha and beta errors. In clinical medicine, we know that we would
      rather make errors of commission rather than omission, and I wonder
      if the ratio of 4:1 for beta to alpha error thresholds is about the
      same ratio that we would choose for commission versus omission, but
      to my knowledge, this has never been quantified. For rejecting a
      diagnosis, I would submit that the probability does need to be less
      than 5%. And a diagnoses with a probability of greater than 20% would
      be very much in play.
      What would the threshold be for rejecting the diagnosis of CAD for a
      patient with chest pain? If we assume that it is <0.05, we can back
      calculate using likelihood ratios to determine what tests and what
      pretest probabilities will get us there. For EKG stress tests with a
      sensitivity of 67%, specificity of 72% and a negative likelihood
      ratio of 0.46, you would have to start with a pretest probability of
      less than 10% to get a post test probability of less than 5%. No
      wonder we don’t use EKG stress tests much anymore, even though they
      are cheap. An imaging stress test, however, has a negative LR of
      0.12. To get to <0.05, you have to start with a pretest likelihood of
      <30%. For patients with a higher prior probability, even a nuclear
      stress test won’t quite get you to our arbitrary threshold for
      dismissing CAD.
      I had a patient recently with exertion chest pain with some typical
      and some atypical features. Her prior probability was about 50% (54%
      from the Diamond and Forrester paper). She had a negative nuclear
      stress test. Because of persistent unexplained chest pain, I
      performed a cardiac cath. She had a severe left main lesion (causing
      balanced defect, which is a known source of false negative nuclear
      stress tests). it was only through persistence, and the knowledge
      that a negative nuclear stress test doesn’t mean 0% posterior
      probability of CAD that we avoided a missed diagnosis and a serious
      mistake. For patients with a pretest probability in the 50% range,
      you either need a very strong test, or several independent tests to
      rule out a diagnosis. If you can’t definitively rule out a diagnosis
      like CAD, you need to follow up and keep thinking about it.

      John

      John E. Brush, Jr., M.D., FACC
      Professor of Medicine
      Eastern Virginia Medical School
      Sentara Cardiology Specialists
      844 Kempsville Road, Suite 204
      Norfolk, VA 23502
      757-261-0700
      Cell: 757-477-1990
      jebrush at me.com



      On Oct 10, 2015, at 7:20 PM, Mark H Ebell <ebell at UGA.EDU> wrote:

      Our study looked at chest pain, suspected DVT, cough in physicians in
      US and Switzerland.

      Rob, we should talk.

      Mark

      From: "Hamm, Robert M. (HSC)"
      Date: Saturday, October 10, 2015 at 6:48 PM
      To: Society to Improve Diagnosis in Medicine, Mark Ebell
      Subject: RE: [IMPROVEDX] [IMPROVEDX] IOM report is released -
      Diagnosis in actual practice

      I have done a survey on “what is the threshold” for giving
      antibiotics for a teenager with strep, with clinicians and patients.
      First, they don’t consciously have thresholds; second, the thresholds
      produced when asked to just the benefits and harms vary widely
      between people; third, they differ within people when the question is
      asked in different ways (decomposed to different extents). Fourth,
      after dropping responses that just don’t make any sense whatsoever,
      the lowest thresholds are those of the 3rd year medical students.
      (lower than patients and first year medical students; lower than
      residents and practicing clinicians).  Poster will be presented at
      Society for Judgment and Decision Making, November, Chicago.

      I would be very interested if there were other studies making these
      comparisons, using different clinical problems.

      Rob Hamm, PhD
      Clinical Decision Making Program
      Department of Family and Preventive Medicine
      University of Oklahoma Health Sciences Center.

      From: Mark H Ebell [mailto:ebell at UGA.EDU]
      Sent: Saturday, October 10, 2015 5:06 PM
      To: IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG
      Subject: Re: [IMPROVEDX] [IMPROVEDX] IOM report is released -
      Diagnosis in actual practice

      I think an interesting area of study is: what are the test and
      treatment thresholds of patients vs physicians? We published a
      methodology for determining thresholds, and it could be used for that
      purpose.

      Ebell MH, Locatelli I, Senn N. A novel approach to the determination
      of clinical decision thresholds. Evid Based Med. 2015 Mar 3. pii:
      ebmed-2014-110140. dos: 10.1136/ebmed-2014-110140.

      Mark

      From: robert bell
      Reply-To: Society to Improve Diagnosis in Medicine, robert bell
      Date: Saturday, October 10, 2015 at 5:15 PM
      To: "IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG"
      Subject: Re: [IMPROVEDX] [IMPROVEDX] IOM report is released -
      Diagnosis in actual practice

      It brings up the idea that could Physicians/HCPs be more open with
      patients and provide a disclaimer of sorts or just information that
      takes probability into consideration and how difficult it is to make
      a diagnosis with certain rare conditions and suggest a way forward if
      a solution/diagnosis is not accomplished in a reasonable period of
      time?

      Rob Bell, MD.


            On Oct 9, 2015, at 10:16 AM, John Brush <jebrush at ME.COM> wrote:

            Mark Ebell’s insightful email points to the absurdity of not
            thinking probabilistically. The probabilities that skilled
            clinicians use in an intuitive fashion in practice are derived
            from scientific evidence and experience (experiential
            knowledge). I am a big believer in evidence-based medicine.
            Without the scientific underpinnings for our clinical
            activities, and explicit acknowledgement of where the science
            is lacking, we would be adrift.
            In David Sackett’s original BMJ article on evidence-based
            medicine, he promoted the use of the best available scientific
            evidence "especially from patient centred clinical research
            into the accuracy and precision of diagnostic tests.” He
            included with his book a nomogram that a clinician could use to
            incorporate likelihood ratios for diagnostic tests with prior
            probabilities to yield a posterior probability for a single
            patient undergoing a single test. To him and other EBM
            founders, probability was the very foundation of statistical
            inference and evidence-based medicine.
            In my book, I stated "We can make highly accurate actuarial
            predictions for populations, but we have trouble even
            comprehending what probability means for a single patient or
            event.” I think this email trail points to the difficulty of
            thinking about probability in medicine. I am concerned that Dr.
            Jain’s paper only adds to the confusion. I would submit that in
            every one of the CPCs that Dr. Jain refers to, the discussant
            makes a statement like, “I think the most likely diagnosis
            is….” The statement "most likely" is another way of saying
            "most probable." Dr. Jain’s statement that probability is only
            a theoretical consideration and is not used in the practice of
            medicine is, I think, absurd. Not acknowledging the uncertainty
            in medicine through some statement of probability (which is
            simply a way to quantify uncertainty) leads to an illusion of
            certainty, arrogance on the part of the practitioner, and
            unrealistic patient and family expectations.
            In my book, it took me 5 chapters to fully develop the idea of
            probability and how it should be used to think about the
            diagnosis and treatment individual patients. This is tough to
            think about and comprehend and I think it can be misrepresented
            in an email listserv.
            For excellent reading on probability, I would suggest Ian
            Hacking’s “An Introduction to Probability and Inductive Logic”
            or Gerd Gigerenzer’s “Risk Savvy: How to Make Good Decisions”
            or “Calculated Risks: How to Know When Numbers Deceive You.”
            Ian Hacking and Gerd Gigerenzer participated in a year long
            sabbatical with other philosophers, scientists, and cognitive
            psychologists where they explored the meaning of probability.
            Hacking has also written “The Taming of Chance” and “The
            Emergence of Probability.” Girgerenzer has also written “The
            Empire of Chance: How Probability Changed Science and Everyday
            Life” for more in-depth reading.
            In clinical medicine, we use conditional probability every day,
            but because the exact numbers are only estimates, we actually
            use a heuristic called anchoring and adjusting. We use reason
            every day, but because the ultimate truth may be unknown, we
            use a type of reasoning called abductive reasoning. (My
            spell-checker incorrectly changed the spelling to adductive
            reasoning in my prior email.) Abductive reasoning, described by
            Charles Saunders Peirce, is "reasoning toward the most
            plausible hypothesis." When we start the diagnostic process, we
            are dealing with multiple hypotheses (plausible conjectures).
            We work through the process toward the most plausible
            hypothesis and, again, the term “most plausible" implies some
            concept of relative probability. With abductive reasoning, we
            blend both inductive reasoning and causal reasoning to make an
            argument (meaning a logical statement) that combines both
            probability and pathophysiologic rationale.
            As W. Edwards Deming said, "if you don’t understand the process
            of what you are doing, you don’t know what your are doing.” It
            is important for clinicians to have a better understanding of
            the process of making a diagnosis. By developing and using good
            habits based on a deep understanding of process, the clinician
            will have the best chance of making the correct diagnosis, as
            reliably as humanly possible.
            My apologies about the long email, but I am very serious and
            passionate about improving the quality of medical decisions.
            John

            John E. Brush, Jr., M.D., FACC
            Professor of Medicine
            Eastern Virginia Medical School
            Sentara Cardiology Specialists
            844 Kempsville Road, Suite 204
            Norfolk, VA 23502
            757-261-0700
            Cell: 757-477-1990
            jebrush at me.com



            On Oct 8, 2015, at 2:54 PM, Mark H Ebell <ebell at UGA.EDU> wrote:

            So, I should order a chest CT for every patient with cough, to
            rule out lung cancer.

            And I should order a stress thallium for every single 25 year
            old with chest pain that appears to be musculoskeletal, so I
            don’t miss the rare MI.

            And of course I should get a CT or MRI for every patient with a
            headache, to not miss the rare (and generally untreatable) CNS
            cancer.

            Do you realize the cost and harm of this approach? The
            complications of invasive tests and biopsies and follow-up that
            go nowhere? The false alarms? Radiation?

            But at least you won’t successfully sue me. I guess that’s all
            that matters.

            Mark

            —
            Mark H. Ebell MD, MS
            Professor of EpidemiologyUniversity of Georgia
            Editor, Essential EvidenceDeputy Editor, American Family
            Physician
            ebell at uga.edu


            From: Phillip Benton
            Reply-To: Society to Improve Diagnosis in Medicine, "
            pgbentonmd at AOL.COM"
            Date: Thursday, October 8, 2015 at 1:17 PM
            To: "IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG"
            Subject: Re: [IMPROVEDX] Fwd: [IMPROVEDX] IOM report is
            released - Diagnosis in actual practice

            I am an experienced  physician-attorney (Medicine 54 Years, Law
            44 years) teaching Medical Malpractice at a top tier law school
            for almost 20 years.
            Relevant to this discussion is the fact that missed or delayed
            diagnosis tops the list of causes for awards to injured
            plaintiffs at mediation or in jury trials. Accounts of serious
            medical error by the Institute of Medicine (1999) and the
            Journal of Public Safety (Sept, 2013) document missed or
            delayed diagnosis as a leading cause of preventable harm. The
            IOM estimate of up to 98,000 preventable deaths per year means
            one every 5 minutes 22 seconds; Dr. John James' evidence-based
            2013 update of up to 440,000 preventable deaths per year equals
            one every 72 seconds.
            One standard approach by the plaintiff''s attorney is to  have
            the defendant physician or defense expert witnesses agree that
            it is important to make a differential diagnosis, and then to
            first rule out the most serious and dangerous diagnoses on that
            list. In other words it is not the odds but it is the stakes
            that matter most. Greater experience of a physician may move
            this process from System II (rational) toward System I
            (intuitive) thinking, but the point is that juries (i.e.,
            patients) routinely agree that you should always deal with  the
            most important things first.
            A common expression heard when an uncommon disease is
            misdiagnosed is that "When you hear hoofbeats you think of
            horses, not zebras." The savvy attorney will then then ask "And
            how do you tell the difference? (pause) You look!"  Adequate
            testing to first rule out life-threatening conditions,
            treatable if caught early, may often allow a successful
            defense.

            Phillip G Benton, MD, JD
            Atlanta Georgia

            -----Original Message-----
            From: Bob Latino <blatino at RELIABILITY.COM>
            To: IMPROVEDX <IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG>
            Sent: Thu, Oct 8, 2015 10:55 am
            Subject: Re: [IMPROVEDX] Fwd: [IMPROVEDX] IOM report is
            released - Diagnosis in actual practice
            I am not a physician nor a clinician, so I come at this issue
            basically from the perspective of a patient.

            When the physician becomes the patient, what is the expectation
            of them towards their care provider in terms of their
            diagnosis?

            Physicians themselves would obviously be more critical of their
            peer's diagnosis when their lives are involved, because they
            are 'insiders' and know the probing questions to ask about how
            the diagnosis was derived.  What are those questions?  What
            should the non-clinical patient be asking of their doctors when
            they provide a diagnosis?

            I am in the investigation business and work in aviation,
            nuclear power, military and other potentially life-threatening
            businesses.  Many in these businesses have to make spur of the
            moment decisions (diagnosing the problem) and then quickly act
            on it.

            I will take pilots for instance.  I know healthcare has taken
            an interest in Crew Resource Management (CRM) from the training
            that pilots receive about effective cockpit communications and
            teamwork.  They too have to quickly make a diagnosis and act on
            it accordingly.

            The difference between a pilot and a doctor in these situations
            is that the pilot and crew's lives are at stake (along with the
            passengers) as well, based on the accuracy of their diagnosis,
            decisions and actions.

            Given this informative debate about probabilities and looking
            at situations/patients singularly versus as a population, how
            does a pilot make their quick assessment versus a doctor and
            their diagnosis?  Does the fact the pilot's life is at stake
            differ in their decision as opposed to a doctor, whose life is
            not likely at stake based on their decision?  Does it matter?
            Should it?


            Robert J. Latino, CEO
            Reliability Center, Inc.
            1.800.457.0645
            blatino at reliability.com
            www.reliability.com

            From: Jason Maude [mailto:Jason.Maude at ISABELHEALTHCARE.COM]
            Sent: Thursday, October 08, 2015 10:09 AM
            To: IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG
            Subject: Re: [IMPROVEDX] Fwd: [IMPROVEDX] IOM report is
            released - Diagnosis in actual practice

            Although this is a very stimulating debate, I am struggling to
            understand how relevant it actually is to the diagnosis of
            individual patients as a key additional variable will always be
            the personal consequences of a wrong decision.  The key
            difference with a probabilistic approach in life assurance or
            similar versus diagnosis of a particular patient has to be the
            consequences of getting it wrong. This means that nobody is
            likely to follow a purely probabilistic approach if they know
            the patient might die if they didn’t check for something even
            if it was a lower probability. The odds of winning the lottery
            are ludicrously bad but because the prize is so big (upside
            consequences) people still try their luck. Personal
            consequences will always seriously affect rational calculations
            of probability.


            Jason Maude
            Founder and CEO Isabel Healthcare

            From: "Jain, Bimal P.,M.D." <BJAIN at PARTNERS.ORG>
            Reply-To: Society to Improve Diagnosis in Medicine <
            IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG>, "Jain, Bimal P.,M.D." <
            BJAIN at PARTNERS.ORG>
            Date: Thursday, 8 October 2015 12:13
            To: "IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG" <
            IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG>
            Subject: Re: [IMPROVEDX] Fwd: [IMPROVEDX] IOM report is
            released - Diagnosis in actual practice

            We can only comment on and critically evaluate material that is
            published. I find it simply amazing that a probabilistic
            approach in which probability is evidence has not been employed
            in even a single amidst hundreds of published CPCs and clinical
            problem solving exercises. Dr. Brush dismisses CPCs as
            artificial, pedagogical exercises employing System 2 thinking
            over days or weeks. This is all the more reason to employ a
            probabilistic approach as the discussants then have plenty of
            time to estimate prior probabilities and calculate posterior
            probabilities. This is not done simply because this approach
            has not been found useful for diagnosis. Some time back, I
            carefully examined 50 consecutive CPCs in NEJM from July 2013
            to OCTOBER 2014. I found the word probability mentioned only
            once in these 50 CPCs. If Dr. Brush thinks this approach is
            suitable only for System 1 thinking in diagnosis ,Croskerry has
            pointed out the danger of such thinking in causing diagnostic
            errors. At present, the emperor does not appear to have any
            clothes with regard to probabilistic approach to diagnosis in
            these exercises. What is  needed ,I think are head to head
            observational or experimental studies comparing usual to
            probabilistic approach in real patients.

            The adage ‘Common things are common’ is useful only in
            indicating chance of a disease in a given patient. Certainly,
            we should look for a common disease first as it has the
            greatest chance of being found. The problem arises when a
            frequency or probability is taken as evidence for a disease.
            There is little doubt in my mind, diagnostic errors due to
            failure to suspect a disease in patients with atypical
            presentation in studies of Hardeep Singh and John Ely arose
            from interpreting low prior probability as absence of evidence
            for the disease.

            In discussion about STEMI, Dr. Brush rightly deals with all
            patients with STEMI regardless of  prior probability in the
            same manner by taking them all for cardiac cath. His accuracy
            rate of acute MI of 85 percent in these patients is close to
            the rate of 90 percent in my paper. If he were to analyze his
            data he would find the majority of patients with acute MI to
            have intermediate or high prior probability.

            I refer the Central Limit Theorem with regard to distribution
            of prior probability which is a continuous variable.

            The main problem with a probabilistic approach is that it takes
            probability as evidence in a given individual patient while it
            is true only in groups of patients. There is no proof that it
            improves diagnosis in actual practice. Its use appears to have
            become a dogma which is hindering efforts to reduce diagnostic
            errors. It is only by looking at diagnosis in actual practice
            such as in studies of H. Singh and J. Ely and analyzing results
            without putting on probabilistic  glasses that we shall make
            progress.

            I mention three examples from history of science of dogmatic
            beliefs hindering progress which was made only when phenomena
            as they occur were analyzed.
            1.      Since the time of Plato, the belief in planetary orbits
            being circular due to perfection of a circle as a geometrical
            figure. All contrary observations were explained away by
            drawing circles(epicycles) within circles. It was only two
            thousand years later that Kepler determined the orbit of Mars
            to be an ellipse when he actually observed and analyzed its
            movement.
            2.      Since the time of Aristotle, every movement was
            believed to require a mover. Contrary observations such as
            flight of an arrow were explained away in an absurd manner.
            Again, about two thousand years later, the true law of motion,
            that it is change in motion and not motion itself that requires
            a force was discovered when Galileo observed and analyzed
            actual motion of rolling balls.
            3.      And nearer to our age, there was a widespread belief in
            Absolute Time since Newton declared it to exist in the 17th
            century. It was only in early 20 the century this belief was
            overthrown by Einstein by his insightful analysis of actual
            time in terms of clocks and trains.


            Bimal


            Bimal P Jain MD
            Pulmonary-Critical Care
            North Shore Medical Center
            Lynn MA 01904


















            From: John Brush [mailto:jebrush at ME.COM]
            Sent: Saturday, October 03, 2015 8:58 AM
            To: IMPROVEDX at LIST.IMPROVEDIAGNOSIS.ORG
            Subject: Re: [IMPROVEDX] Fwd: [IMPROVEDX] IOM report is
            released - Diagnosis in actual practice

            I’m afraid that I can’t agree with Dr. Jain’s argument. I think
            his argument is circular, difficulty to follow, and selectively
            self-serving.
                        We have an adage in medicine: “Common things are
            common.” Otherwise, every diagnostic exercise would become a
            wild goose chase, leading us to look into every remote
            possibility every time. Having said that, I can also say that
            if we collect cases over time, uncommon things become common.
            Someone somewhere will eventually win the lottery. Uncommon
            diagnoses do occur eventually. But the exceptions should not
            define the rules.
                        The STEMI case that Dr. Jain presents proves my
            point. I am in interventional cardiologist who frequently takes
            patients with suspected STEMI to the cath lab for intervention.
            I have been getting direct feedback on these cases for about 25
            years. I can tell you that there is a false positive rate of
            about 15% among STEMI alerts that are taken to the cath lab
            (numerous reports in the literature confirm that estimate). We
            allow that false positive rate because we make a subjective
            calculation of expected value. Even if a patient has a
            relatively low initial prior probability of STEMI, like Dr.
            Jain’s example, we don’t want to miss a serious diagnosis like
            a STEMI. The EKG findings change the probability estimate and
            make a STEMI quite plausible in such a patient. In a patient
            like Dr. Jain’s example, we know that there is about a 50-50
            chance of finding an occluded artery, which is certainly high
            enough to activate the cath lab. And sure enough, over time,
            50% is about the frequency that we find in such patients.
                        Dr. Jain references central limit theorem. That
            theorem applies to probability for a continuous variable, and
            states that for any distribution, the sample means of repeated
            samples will become a normal distribution. I’m not sure I
            follow his argument that it applies to a probability
            distribution of categorial variables. A diagnostic category is
            a countable variable. Kolmogorov’s principles, however, do
            apply. The probabilities of all of the possibilities do add up
            to one, if they are all independent. General knowledge of these
            probability principles can help us organize our thinking.
                        When we see a patient with chest pain in the ED, we
            start to narrow the sample space by asking questions and making
            observations. For example, we can eliminate the possibility of
            a stab wound very quickly by noticing that there is no knife in
            the chest. Through early hypothesis generation, we narrow the
            range of possibilities to the point were we can start the

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