In last week’s Practice Perfect 538 - Rational Diagnosis Part 1: Clinical Scripts, I presented the case for an orderly rational methodology for arriving at a diagnosis. I showed the common Clinical Scripts method, where we use our powers of pattern recognition to compare the current clinical presentation to other similar presentations which we’ve seen. As mentioned, this method works well for the majority of our common diagnoses and decisions, but falls flat in the rare or uncertain situation. I left you last week intellectually hanging on the cliff's edge with Bayes’ rule as an alternative method to figure out diagnoses and testing. In Part 2, I’m going to help you learn this new method, and its important medical corollary, pretest probability, which together will provide you with a new orderly, rational approach to formulating a diagnosis when you encounter less common presentations.

Let’s Begin with This Example

Some years ago, I had a patient with a second toe ulcer that was admitted for cellulitis and possible osteomyelitis. Prior to my being consulted, the medicine service had obtained an MRI of the patient’s foot (at one of my hospitals, they like to order MRI's for everything it seems). The MRI was read as osteomyelitis of the head of the second toe proximal phalanx. From my clinical examination, I had a low suspicion that the patient actually had osteomyelitis, so during the surgery (an arthroplasty of the toe) I sent the specimen for cultures and pathology. Luckily for my patient, my diagnosis was correct, and she kept the toe. Did the MRI provide any help with this patient’s medical care?

Bayes’ Theorem

Bayes’ rule is a complicated method of statistics and probability, but without getting mathematical (thank God!), we can discuss it in more general terms. Simply put, Bayes’ rule (or theorem) allows us to describe the probability of a particular event occurring based on our prior understanding of that event (termed conditional probability). It is a way for us to use new information about an event to update our knowledge. We actually use this method intuitively without even realizing it, so don’t stop reading yet!

Let’s take my example above and pretend for a minute that the medicine team hadn’t already ordered the MRI. Instead, while consulting me, they asked if they should order the MRI (as they should have done).

The question then becomes “What are the chances that this diabetic patient with a toe ulcer has osteomyelitis?” If, after examining the patient, I thought the chances were high – let’s say I did a probe-to-bone test during my exam and it was positive – then my clinical suspicion of osteomyelitis would be high before ordering any other tests. This is also called pretest probability.

One quick comment here. Understanding how the probe-to-bone test would affect a clinician’s judgment is necessary to come up with a reasonable pretest probability. For example, I know, based on Grayson’s work¹ that the probe-to-bone test has an 89% positive predictive value for osteomyelitis in acutely ill, infected, hospitalized patients. On the other hand, I also must be aware that this same positive predictive value drops significantly in outpatients with noninfected diabetic foot ulcers, while the negative predictive value (the ability to exclude the disease) is much higher with a negative test result.² Without knowing this information, my judgment is likely to be skewed. This is why we must continue to read the evidence from the research literature.

Pretest Probability

In 1998, Wrobel and Connolly used a Bayesian approach to answer the very question I’ve asked above.⁴ They used this approach to argue that pretest probability is more important than the specific tests ordered to diagnose bone infections in the diabetic foot.

They performed a Medline search and found 17 studies that discussed the sensitivity and specificity of five tests (probe-to-bone, radiographs, three-phase technetium scan, indium labeled scan, MRI) in diagnosing osteomyelitis compared with bone biopsy, the “gold standard”.

Here’s what they found (table abstracted from reference 4):

The authors then used Bayes’ theorem to calculate the probability of bone infection given positive or negative test results. The authors used intermediate pretest probabilities of 0.25 – 0.50, since these are the most likely times when clinicians would order testing (if you were 100% sure of a diagnosis [pretest probability of 1] why would you bother ordering the test?). Again I’m not going to show the math; feel free to read the study itself for further detail.

To boil down and summarize their results, these researchers found that with a high pretest probability, the probe-to-bone test performed about as well as all the tests in predicting osteomyelitis, and a negative MRI was the best at predicting the absence of osteomyelitis. The pretest probability was more important for determining the likelihood of this diagnosis (the posttest probability) than any of the test parameters such as sensitivity and specificity. They argued that more research needs to be done to help clinicians better estimate pretest probability, rather than the current research focus on diagnosis and treatment. Unfortunately, 18 years later, it doesn’t appear their recommendations were heeded.

Now, there are a few ways for us to determine a pretest probability.³ One of those is personal experience, the recounting of Clinical Scripts, which we discussed last week. Unfortunately, cognitive and social sciences have found humans are prone to many biases that affect our judgment. We can also use practice databases which track data like diagnosis codes. Of course, these must be available for our use. We can also look up the prevalence of certain diseases through direct research. Clearly this requires the research to have been performed in the first place. Finally, we may also have access to population statistics on certain diseases. Obviously, this requires the disease to be a target for acquiring the statistics in the first place, which will likely leave out some of the more rare diagnoses.

So where does this leave us clinicians in using the Bayesian approach of pretest probability? We can just say, “Forget this!” and go back to guessing based on our biased experience. However, I prefer a more moderate approach of qualitatively estimating pretest probability and using that to determine whether or not to test.

Medow and Lucey⁵ discussed a practical method to determine if further testing is needed.

First, using the best medical evidence and your expertise, categorize your patient’s pretest probability of having the diagnosis as:

Next, if either of the first or last categories are chosen then no further testing is necessary.

Then, if the pretest probability is in the range of the other three categories a test may be beneficial.

Finally, consider the test results as they relate to the likelihood of your diagnosis being the correct one:

In the case of my patient at the outset of this discussion, I would have chosen not to order the MRI because the history and physical examination were more consistent with an ulcer without osteomyelitis (minimal infectious appearance and negative probe-to-bone test). I would have determined the pretest probability as unlikely to very unlikely (estimated less that 10-15%). Knowing that biopsy is a better test than MRI for diagnosis of osteomyelitis and the fact that surgically repairing this patient’s toe deformity would greatly reduce the future risk of ulceration, this approach would have been better than ordering the MRI in the first place. A more rational test choice method would have saved the medical system an expensive test and the patient from a potential amputation if the MRI result would have been acted on thoughtlessly.

A true Bayesian mathematically-oriented approach is unlikely to become popular with those of us in active clinical practice, but a more intuitive approach is very helpful to rationally diagnose and treat our patients.