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Math Errors Can Imperil Patients

How good is your physician at math? Does it even matter? Well, for starters you'd want that doc to administer the right dosage of epinephrine when you or your child desperately need it. Just take a look at In the Lab: Simple Math Errors Can Imperil Patients in today's New York Times:

Researchers tested a group of 28 doctor volunteers using a high-tech

patient simulator. The doctors were told that the patient was a 5-year-old with a potentially fatal allergic reaction to peanuts. This was said to be a medical emergency, and the proper treatment was 0.12 milligrams of epinephrine injected as quickly as possible.

Half the doctors were given a glass bottle of epinephrine labeled “1 milligram in 1 milliliter solution.” The other half had bottles labeled “1

milliliter of a 1:1000 solution” — exactly the same thing but expressed as a

ratio instead of a concentration. In either case, the correct dosage would

be 0.12 milliliters of the solution.

**Eleven of the 14 in the concentration group, but only 2 in the ratio group, calculated the dose correctly.** The concentration group needed an average of 35.5 seconds to make the injection, while the ratio group averaged more than two minutes. **One doctor in the ratio group administered a full milligram of epinephrine, about eight times the correct amount. **

So, you just might want see just how good your physician is when it comes to math. Of course, I would argue that the lab technicians and pharmacists better know their numbers too. According to Dr. Daniel W. Wheeler, an anesthesiologist and clinical lecturer at the University of Cambridge in England, "errors tend to be by factors of 10-- large and potentially dangerous."Just one more reason to make sure your child gets a solid math education. That little person of yours just might want to grow up and be a physician some day.

## 2 comments:

Honestly, I'm a little confused by the math myself; mg are a measure of mass, mL are a measure of volume. It's impossible at first glance to tell what 1 mL in a 1:1000 solution even means. I can understand that this is probably a standard notation among pharmacists, but, really, it's a really stupid one - there are no units! 1:1000 is just a number; unless you know what the 1 and the 1000 are, you can't figure out the concentration.

As it turns out, it's 1 kg per 1000 L - the standard metric units of mass and volume. The problem is that kg and L are way too large to measure dosages of drugs (hence, the 1mg / 1mL notation). It's not surprising that a doctor would find it confusing.

.12mg = x * (1kg / 1000L)

.12mg * (1,000L / 1kg) = x

.12mg * (1,000L / 1kg) * (1,000mL / 1L) * (1kg / 1,000g) * (1g / 1,000 mg) * = x

.12mg * (1,000L * (1000mL / 1L)) * ((1 / 1kg) * (1kg / 1,000g) * (1g / 1,000 mg)) = x

.12mg * (1,000,000mL) * (1 / 1,000,000mg) = x

.12mg * (1,000,000mL / 1,000,000mg) = x

.12mg * (1mL / 1mG) = x

.12mL = x

It's not especially difficult, but it's needlessly complicated even if you did know the units.

Needlessly complicated particularly when someone's life is hanging in the balance.

Given the complexity, it seems almost amazing that eleven of the 14 actually calculated the dose accurately and that only one doctor was absolutely over the top.

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