January 03, 2010

RANDOM: Benford's Law Applied to Health?

Today, I listened to an amazing NPR RadioLab episode titled "Numbers."

In one of the stories in this episode, Jad and Robert Krulwich educated me on an interesting mathematical phenomenon called Benford's Law. Simply stated, Benford's Law states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit of a number is "1" almost one third of the time, and larger digits occur as the leading digit with lower and lower frequencies, to the point where 9 as a first digit occurs less than one time in twenty. This is completely contrary to the expectation that the number 9 or 8 should occur equally as frequently as 1 or 2.

(From "The First-Digit Phenomenon" by T. P. Hill, American Scientist, July-August 1998)

But get this... This law holds true whether talking about random samples from a day's stock quotations, a tournament's tennis scores, the numbers on the front page of The New York Times, the populations of towns, electricity bills in the Solomon Islands, the molecular weights of compounds, the half-lives of radioactive atoms, and much more.

It seems to me that if the universal natural state of order follows Benford's Law... I wonder whether it also holds true for the human body...

I did a pubmed search and it seems that there have been a few researchers who had the same idea, most applied only to basic biological processes:

- Biologic kinetic rate parameters follow Benford's Law (abstract)
- mRNA transcription data from a wide range of organisms and measured with a range of experimental platforms show close agreement with Benford's law (abstract)
- Different states of anesthesia can be detected by Benford's Law (link)

Just for giggles and kicks, I looked up normal bloodwork values for a human being. This website nicely listed the most common normal values. I than jotted down the frequencies of the first integer of all the lab values listed and here's what I came up with:

#1 (30.5%)
#2 (17.1%)
#3 (10.2%)
#4 (10.2%)
#5 (7.3%)
#6 (7.3%)
#7 (6.5%)
#8 (5.8%)
#9 (5.1%)

Amazingly... though the frequencies don't match up perfectly, they do come eerily close to Benford's Law.

With larger lists of numbers, the approximations may come even closer. Potential neat project for a student, eh?
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Fauquier ENT

Dr. Christopher Chang is a private practice otolaryngology, head & neck surgeon specializing in the treatment of problems related to the ear, nose, and throat. Located in Warrenton, VA about 45 minutes west of Washington DC, he also provides inhalant allergy testing/treatment, hearing tests, and dispenses hearing aids.

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