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Using Probability in Medical Diagnosis: A Headache Example
Experienced clinicians begin the process of making a diagnosis
upon first laying eyes on a patient, and probability is one of
the main tools they use in this process. A glimpse "behind the
scenes" from the point of view of a diagnosing physician might
help to explain an otherwise mysterious process.
The diagnostic process can begin even before laying eyes on the
patient. As an exercise (and to prove a point) I ask medical
students who are with me in the office to diagnose the patient
we haven't seen yet who is still in the waiting room. Of course,
they look at me like I'm crazy. But I tell them that we already
know a lot about the patient and can make some educated guesses.
For example, we might already know that the patient is a
34-year-old woman referred by a family doctor because of
headaches.
So what have other women in their thirties referred to me for
headaches ended up having as their diagnosis? In my neurology
practice, as well as in those of most other headache
specialists, about a third (33%) have migraine, another third
have medication-overuse headaches (in which the treatment has
become the problem instead of its solution), and the remaining
third fall into an "everything else" category that includes
tension-type headaches, arthritis of the neck or jaw-joints,
sinus disease, tumors, etc. So before seeing the patient I'm
already able to identify the two most likely diagnoses and
assign an initial probability for each.
These starting-point likelihoods are called "anchor"
probabilities. During the subsequent history, examination and
supplemental testing (if necessary) the anchor probabilities
will undergo a series of upward and downward adjustments
according to what the patient has to say and what does or does
not turn up on her physical examination and testing. The
physician individualizes the questions asked and items examined
so that the outcome of each query forces one diagnosis to be
more likely and another to be less likely. Thus, diagnosis is a
dynamic and sequential process.
We invite the woman into the examining room and listen to her
story. In the headache example given, one key piece of data is
how many days per month she takes an as-needed medication - for
example, aspirin, acetaminophen or a prescription drug. If she
takes as-needed medicine more days than not and has been doing
so for a matter of months, then the initial 33% anchor
probability of medication-overuse headaches gets adjusted upward
and the initial anchor probability of uncomplicated migraine
moves downward. This, of course, is just a single distinguishing
feature, and cannot be relied upon to tell the whole story. The
physician gathers many such data points to refine the diagnosis.
The physical examination provides another source of facts to
distinguish among still-viable possibilities. If my patient has
migraine or
medication-overuse headaches, she might have tender
muscles in her scalp and neck but should not have a blind spot
in her visual fields, slurring of her speech or clumsiness on
just one side of her body. These findings, if present, would
cause the probabilities of migraine and medication overuse
headaches to be revised downward. By contrast, the probability
of a brain disease - like a tumor, for example - that started
with a low anchor probability would get revised upwards.
If a blood test or a scan is ordered, it is again with the idea
that the test has been individualized to discriminate between
competing diagnoses and re-adjust their relative probabilities.
There is an important principal in medical diagnosis called
Bayes' theorem. In a nutshell, Bayes' theorem states that the
probability of a diagnosis after a new fact is added depends on
what its probability was before the new fact was added. Another
way of saying this is that the same "yes" answer on
history-gathering, reflex result on physical exam or dark spot
on an MRI scan has different implications in different people.
The meaning of each depends on its context. Yet another
implication of Bayes' theorem is that one can't skip past the
history and examination by ordering a test in isolation and
expect it to make an accurate diagnosis. A test is an answer to
a question. If there was no question, how could the test be an
answer?
Let's say that at a particular point in time we have completed
the diagnostic process for a patient. Then what? By the end of
the diagnostic process the doctor might have a diagnosis that is
nearly 100% likely, but in other cases, the working diagnosis
(number one choice) might still be just 70% or 80% probable,
with a number two choice less likely, but still on the radar
screen. It might make some patients uncomfortable to realize
that the diagnostic process does not lead to 100% certainty in
every case, but a doctor wouldn't be doing a patient any favors
by pushing the analysis past the outcome that the available
information leads to.
When a diagnosis is not 100% likely at the time of initial
evaluation, the patient's course of symptoms over time provides
yet another form of data that can lead to revision of diagnostic
probabilities. Fortunately, in cases involving uncertainty, even
just narrowing down the list of diagnoses to a small number of
concrete alternatives allows the doctor and patient to discuss
reasonable options and make sensible choices.
(C) 2005 by Gary Cordingley
About the author:
Gary Cordingley, MD, PhD, is a clinical neurologist, teacher and
researcher who works in Athens, Ohio. For more health-related
articles see his websites at: http://www.cordingleyne
urology.com and http://www.neurologyartic
les.com
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