Using Probability in Medical Diagnosis

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 principle 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.