Jan 28 2014

Occam’s Razor vs Hickam’s Dictum

Every year since 1998 Edge magazine asks a large group of public intellectuals a provocative question and then publishes their answers. This year the question is: What Scientific Idea is Ready for Retirement?

Gerald Smallberg (Practicing Neurologist, New York City; Playwright, Off-Off Broadway Productions, Charter Members; The Gold Ring) gave as his answer, “The clinician’s law of parsimony.” He writes:

“As an absolute, the Law of Parsimony is floundering. Not because it is aging poorly, but rather because it is being challenged more and more by the complexity of the real world and its need for a valid counterweight. From my vantage point as a physician in the practice of clinical neurology, its usefulness, which has always been a guiding principle for me, can easily lead to blind spots and errors in judgment when rigidly followed.”

He defines Occam’s razor as:

“This law states that the most simple of two competing theories should be the preferred one, and that entities should not be multiplied needlessly.”

The second part of this definition is the more precise, but Dr. Smallberg mainly discusses the first part. I have written about Occam’s razor in the past because it is frequently misrepresented, in a subtle but important manner. I believe that Dr. Smallberg is committing this same error.

Occam’s razor is often presented as the first part of the definition above – when there are multiple possible answers, the simplest should be preferred. However, the direct quote from William of Ockham is this:

“Numquam ponenda est pluralitas sine necessitate [Plurality must never be posited without necessity].”

Dr. Smallberg correctly identifies the flaw in applying the incorrect version of this principle – often, especially in medicine, the simplest answer is not the correct one. In medicine “simplest” is often translated into “fewest number of diagnoses.” He quotes Hickam’s Dictum which states that “a patient can have as many diagnoses as [she] damn well pleases.”

The fix, however, is not in concluding that Occam’s razor has limited utility, but rather in understanding what the principle actually is.

Stated another way – Occam’s razor is the principle that the introduction of new assumptions should be minimized. “New assumptions” should not be conflated with “additional diagnoses.” That is the error.

Dr. Smallberg gives an example case of a woman who has many simultaneous problems, several of which can relate to her chief complaint, difficulty walking. He chose a problem that is often multifactorial, but it serves as a useful example of his point.

Here’s the precise flaw in his argument – as we get older we tend to accumulate diseases and disorders. Further, one disease or condition can predispose to or lead directly to another – diabetes can cause neuropathy which can cause gait difficulty. We can add to this that some conditions are extremely common.

A patient who presents with known diseases, is at high risk for certain conditions, or complications of their known diseases is going to have multiple diagnoses. We do not have to introduce any entirely new assumptions. We can extrapolate directly, and with high probability, from what is known. In such a case, therefore, using multiple diagnoses to explain a patient’s presentation does not violate Occam’s razor.

In fact, Occam’s razor may prefer that we explain a patient’s presentation with three or four common or related disorders, rather than one extremely rare disease. The rare disease is introducing a giant new assumption, while the four common conditions to which the patient is at high risk are not really introducing anything new.

What a clinician should not do (and which does violate Occam’s razor) is introduce an entirely new disease or condition just to explain each individual sign or symptom of a patient.

In the end Occam’s razor is all about probability, and experienced clinicians understand and use probability in what is called their “differential diagnosis.” What clinicians do is try to think of every plausible way to explain the patient’s total presentation, and then they rank the possibilities from most likely to least likely. This helps prioritize what tests to order and treatments to give.

In ranking how likely each possibility is, you can imagine adding up all the new assumptions that each diagnosis would represent, both number and magnitude, resulting in a total assumption burden. Therefore, one entirely new and extremely rare diagnosis might render one explanation far less likely than using three new but very probable new diagnoses.

The more common a diagnosis, the less of a new assumption burden it represents, and the less it violates the principle of parsimony. Also, diagnoses may exist in a chain of causality: obesity leads to diabetes which can cause neuropathy which may result in gait difficulty. So, even though I may be giving the patient four diagnoses, they all flow from the first, and the total burden of new assumptions is low.

When viewed in this way, minimizing the total burden of new assumptions (accounting for both number and magnitude) Occam’s razor is a very useful logical tool for the clinician (or any investigator) and does not suffer the limitations imagined by Dr. Smallberg.

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