Without evidence of benefit, an intervention should not be presumed to be beneficial or safe.

- Rogue Medic

More on Drug Calculations

I am making a pun at my own expense. Not More on Drug Calculations, but Moron Drug Calculations.

And I am the moron.

In my last post, Current Drug Shortages, I was pointing out ridiculing concerns about the use of 1:1,000 epinephrine IV, since it should never be given through an IV to a live patient, except as a drip. This is true. It is not considered wrong by the FDA (Food and Drug Administration), but that is something the FDA should change.

The problem is with my calculation of the drip rate. I wrote, not just once, that putting 1 mg of epinephrine in 250 ml NS (Normal Saline) would produce a concentration of 4 mg/ml.

I hope that everybody reading this has noticed the mistake I made. You don’t need to be a math whiz to be able to figure out that when you dilute 1 mg/ml by adding 250 ml, you do not get a more concentrated solution. Dilution produces a less concentrated solution.

If the same mistake were being made by a student in an ACLS (Advanced Cardiac Life Support) class, and this mistake has been made plenty of times, I would ask the student some questions, because many of these mistakes cannot be made with the supplies that are in a crash cart or EMS drug bag.

For example, plenty of students have stated that they would give one gram of epinephrine. I have never seen a crash cart or EMS drug bag with even 100 mg of epinephrine. You have to do some restocking to get that much. In the hospital, that means somebody running to the pharmacy to get 1,000 mg. If they state 1:10,000, that means 10 liters, and it is unlikely that the pharmacy carries epinephrine in 1:10,000 concentration in liter containers. 1,000 preloaded syringes of 1:10,000 epinephrine may be more than is available in the pharmacy. Anyway, once I state, A coworker points out that we do not have enough epinephrine to give 1 gram of 1:10,000 epinephrine, the student usually realizes the mistake and corrects the mistake without any further need for hint or for explanation.

I have seen several instructors immediately state that the student killed the patient. I don’t know what kind of dream world these instructors live in, but it appears to be a sadistic one with no grasp on the reality. If the student does not have the capability to actually give 1 gram of epinephrine, then how can the student kill the patient with 1 gram of epinephrine?

I hear the excuse that the student has to learn somehow. This suggests that pointing out the drug calculation is not embarrassing enough to make it memorable. This suggests that a petty and unrealistic comment by an instructor is in some way an example of great teaching. It is not.

However, what I did was much worse than a student making a simple mistake in a stressful moment – a mistake that could not lead to the administration of the wrong dose to the patient. Well, JCAHO might try to make it possible, just so they can penalize people for this.

What I did was tell people that this impossible concentration is the correct concentration.

This is going to mislead and confuse people. It will get others to laugh at me. I should be decreasing confusion, not contributing to confusion. I do not have the same excuse as a student being tested in an ACLS class. I had plenty of time to check everything and in the unreality of the internet anything is possible, right up until it is tried in the real world.

There is one other problem with the drug concentration of 4 mg/ml.

The concentration of 1:10,000 epinephrine is 0.1 mg/ml. I cannot create a concentration of 4 mg/ml, unless I add even more concentrated epinephrine to this 0.1 mg/ml concentration. 4 mg/ml is 40 times more concentrated than 1:10,000 epinephrine.

If you do not understand this, assume that you add 1,000 mg epinephrine to 250 ml NS, you get 4 mg/ml. That works, but only as long as you do not consider the amount of solution that is already included with the epinephrine. For 1:10,000 that means 10 liters of solution with the 1,000 mg, so you do not end up with 4 grams/250 ml or 4 mg/ml. You end up with 1 gram in 10,250 ml or 97.6 mcg (MICROgrams)/ml. Ordinary 1:10,000 epinephrine is 100 mcg/ml (0.1 mg/ml or 100 mcg/ml – not significantly different from what we end up with).

The concentration of 1:1,000 epinephrine is 1 mg/ml. The same concentration problem exists, except that 4 mg/ml is only 4 times more concentrated than 1:1,000 epinephrine.

For 1:1,000, assume that you add 1,000 mg epinephrine to 250 ml NS and you get 4 mg/ml. For 1:1,000 that means 1 liter of solution with the 1,000 mg, so you do not end up with 4 grams/250 ml or 4 mg/ml. You end up with 1 gram in 1,250 ml or 800 mcg (MICROgrams)/ml. Ordinary 1:1,000 epinephrine is 1,000 mcg/ml (1 mg/ml or 1,000 mcg/ml – there is a more significant difference between 800 mcg/ml [0.8 mg/ml] and 1,000 mcg/ml [1 mg/ml]).

Either way, I was suggesting something that is impossible with standard concentrations of epinephrine. It was suggested to me that I was trying to engage in a bit of homeopathy, by pretending that dilution leads to greater strength. 🙁

Dilution does not lead to greater strength.

This is probably the reason that I made this mistake, other than just not thinking, and I wasn’t thinking. We learn the lidocaine clock for calculating concentrations of drips that we use in EMS. Lidocaine commonly comes in a package of 100 mg/10ml for IV push in cardiac arrest. It doesn’t improve outcomes, but that is a different discussion. If you add 100 mg/10ml lidocaine to 250 ml NS, you end up with 100 mg in 260 ml or 3.85 mg/ml. This should also be rounded off to 4 mg/ml, even though it is a much bigger difference from the 4 mg/ml. The reason is that both are not significant differences.

Mixing 1 in 250 will give you a 4/1,000 concentration. Since we can move the decimal (by changing the prefix) to give a 4/1 concentration we need to remember to make sure we are still dealing with the right amounts when we have completed our calculations. Any time we end up with numbers that seem as if they require a lot of drug, or very little drug, we need to consider the possibility, even the likelihood, that we made a decimal point (prefix) error.

Thank you to Matt J for pointing out my huge mistake. I will correct it on the original post, too.


What Math Do We Need To Know?

An interesting and very short – less than 3 minutes – presentation from a professor of mathematics about what we should be teaching in math class.

I can’t leave you hanging like that without telling you a little bit about what 2 standard deviations means. But first you should read what he said in, If Arthur Benjamin got an extra minute on stage ….

Now to what 2 standard deviations means. This is easiest if you look at a bell curve. Bell curves only represent normal distribution. You’ve seen this curve before.

Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for 68.27 % of the set; while two standard deviations from the mean (medium and dark blue) account for 95.45%; three standard deviations (light, medium, and dark blue) account for 99.73%; and four standard deviations account for 99.994%. The two points of the curve which are one standard deviation from the mean are also the inflection points.[1]

Here is another way of looking at the same information, just rotated to the side

The red circles with tails are the Greek letter Sigma, which is the symbol for standard deviation. The data points (dots) on the left are far too few to produce the smooth curve that appears on the right (which is just the bell curve from above with different colors and flipped on its side, so that the standard deviation bars approximately match). No the numbers on the left are not grades of a class from paramedic school before grading on a curve.

Why is it important to understand the concept of 2 standard deviations?

Anything outside of 2 standard deviations is unlikely. Anything outside of 3 standard deviations is rare.

In the video, he mentions the financial mess. One of the big problems was that bankers were making sub-prime loans that initially were just a tiny part of their business. As long as they remained a tiny part of the business, that was not a problem. Grouped in with an overwhelming number of safer loans, they would not present a huge problem, even if they all failed at once.

Mortgage writers were apparently ignoring the increasing proportion of loans that were sub-prime. They went from between 2 and 3 standard deviations to around 1 standard deviation. now it did not even take a coordinated failure of these loans to cause a huge problem, but the mortgage writers kept acting as if things had not changed. They were making their consistent commission. They were selling the risk to people with even less understanding of statistics. On the other hand, they were selling a risky asset, rather than keeping it as an investment. So, maybe they were not so unaware.

When the problem loans were only a few percent of business, the risk was small. You can see from the bell curve, that only a little of the shaded area is there. As the percent of problem loans increased, the chance of many failing at the same time increased. It was not a question of if, but when.

Things changed. Not a little bit, but a lot. The change was ignored.

We do the same thing in EMS in many ways.

We claim that some risk is small, insignificant.

We do this for many things.

We ignore the accumulation of rare, or just unlikely, risks.

We act surprised when the inevitable happens.

We blame someone else.


^ 1 Standard Deviation
All of the graphs are from Wikipedia.


Observations on the NTSB HEMS Hearings

During today’s NTSB hearings[1] there were some interesting comments.

The first speaker, Dr. Ira Blumen,[2] looked carefully at the safety statistics for helicopters and fixed wing aircraft. He compared all types of aircraft safety data. He arrived at a crew fatality rate figure that would make HEMS employment the most dangerous, or second most dangerous job in America. The confidence intervals for this were not given, but the wide range of fatalities, from year to year, make it clear that this is going to be less accurate than many professions with many more employees in that particular field.

The fatality rate is calculated per 100,000 employees per year. There are only 12,000 employees in HEMS, so 1 fatality per year, if the employment level remains steady, equals just over 8 per 100,000. An improvement in safety, that prevents the death of one crew member per year, would have a much more dramatic effect on the fatality rate per 100,000 employees per year. A change that makes HEMS less safe, would have a similarly dramatic effect in making all other dangerous occupations seem safe by comparison.

He proceeded to calculate the death rate for patients. This was less than 1 per 100,000. This is a good thing. one of the reasons is that there are generally 3, or more crew members for each patient on board. another is that there is not always a patient on board, when there is a fatal crash. At the end of his presentation, he tried to compare these numbers to ground ambulance fatalities. He admitted that there are no firm statistics on these fatalities, so he decided to compare all motor vehicle fatalities to all HEMS patient fatalities. He concluded that HEMS transport is much safer.

First, he is comparing things that are not at all related. While it is true that there are no good statistics on ground ambulance fatalities, crew member fatalities, or patient fatalities, these can be estimated. It is wrong that these data are not tracked, but since they are not, we can only estimate the rate. If the numbers of patient fatalities in ground ambulances were comparable to the total motor vehicle fatality rate, there would be hundreds, or thousands of fatalities of EMS patients per year. Are the EMS black helicopters coming down and cleaning up all of these fatalities? Do all of these patients go to Area 51? I do not believe that this is a reasonable way of calculating the risk to ground transport patients. I think it is obvious that this overestimates the fatalities by a huge amount. In a, I used my own method of estimating the crew fatality risk, not the patient risk. The reason was that I was going by the EMS fatality rate. The EMS fatality rate is still not completely accurate, but there are people tracking EMS fatalities. I get emails every time there is a report of an EMS LODD (Line Of Duty Death). The suggestion that the fatality rate can be calculated from all motor vehicle deaths, yet it would not correlate at all with EMS LODDs, is not credible.

He also compares the fatality rate of all of HEMS to the IOM (Institute Of Medicine) iatrogenic death rate of 44,000 to 98,000 patients per year. This produces a number much higher than the overall motor vehicle fatality rate. This seems to suggest that the patient is safer in the helicopter, than in the hospital. It also suggests thsat the patient is safer in the ground transport ambulance, than in the hospital.

Obviously, I need a raise. But why should any of us transport patients to the hospital, if the hospital is so dangerous?

One thing to consider about the iatrogenic deaths – they cover the entire time the patient is in the hospital AND anything that happens that might be related to when the patient was in the hospital. The amount of time a patient is in the hospital is much greater than the amount of time the patient is in the helicopter. Typical patients will probably be spending more time in the waiting room of the hospital, than they will be spending in the helicopter. Maybe we should be comparing the iatrogenic death rate of the hospital waiting room to the fatal crash rate of HEMS. These comparisons are not valid.

But wait, the iatrogenic death rate of HEMS is not even considered in the HEMS fatality rate, unless the patient dies in a HEMS crash. Iatrogenic death for the hospitals includes just about every possible contribution to death that might lead to a preventable death.

Types of Errors


Error or delay in diagnosis
Failure to employ indicated tests
Use of outmoded tests or therapy
Failure to act on results of monitoring or testing


Error in the performance of an operation, procedure, or test
Error in administering the treatment
Error in the dose or method of using a drug
Avoidable delay in treatment or in responding to an abnormal test
Inappropriate (not indicated) care


Failure to provide prophylactic treatment
Inadequate monitoring or follow-up of treatment


Failure of communication
Equipment failure
Other system failure

SOURCE: Leape, Lucian; Lawthers, Ann G.; Brennan, Troyen A., et al. Preventing Medical Injury. Qual Rev Bull. 19(5):144–149, 1993.[3]

All of these conditions apply just as much to patient care in the helicopter as in the hospital. Care in the helicopter is restricted by the environment, so that in-flight assessment and treatment are limited, compared to in-hospital assessment and treatment. There is no consideration of diagnostic, treatment, preventive, or other criteria from HEMS. There is no follow-up of iatrogenic death that may result from HEMS transport. Comparing falling-out-of-the-sky risks, while ignoring all other risks, is very misleading. To be fair, this also ignores the same iatrogenic death contributions that occur in ground EMS transport, which has many of the same limitations on assessment and treatment.

This is not to diminish the rest of what Dr. Blumen said. I think that he did a commendable job when he was looking at the helicopter data. When he was using the helicopter data, he was familiar with the ways that the data might be misleading. He presented appropriate caveats and made it clear when he was drawing conclusions, that others might reasonably disagree with. When he tried to compare the non-HEMS data, he seemed to be adding them as an afterthought. These ground EMS and hospital iatrogenic death data, at least as used in Dr. Blumen’s presentation, are not relevant to the HEMS data.


^ 1 Safety of Helicopter Emergency Medical Services (HEMS) Operations
Public Hearing
February 3–6, 2009
Biographies for the Board of Inquiry and the Technical Panel
Witnesses’ Biographies
Live Webcast – Captioned!
Windows Media Player
Real Player

    • Tuesday 2/3 – 9 am
    • Wednesday 2/4 – 8:30 am
    • Thursday 2/5 – 8:30 am
    • Friday 2/6 – 8:30 am.
    • Archive links will be added after each day’s presentations have concluded

^ 2 Witness #1 Ira Blumen, M.D.,
Director, University of Chicago Hospitals, Chicago, Illinois
Dr. Blumen has been involved in air medical transport since 1985 and has been the program and medical director of the University of Chicago Aeromedical Network (UCAN) since 1987. Before that, he was the medical director of the MedStar helicopter program at St. Mary of Nazareth Medical Center in Chicago. Dr. Blumen served on the Board of Directors of the Association of Air Medical Services (AAMS) and was a founding member, board member, and past-president of the Air Medical Physician Association (AMPA). He has received numerous awards, including the 2004 AAMS Jim Charlson Award, which recognizes an individual for significant contributions to the overall enhancement, development, or promotion of aviation and aviation safety within the air medical transport community. In October 2008, Dr. Blumen received two additional awards for his continued work and dedication to HEMS safety research: the 2008 AAMS President’s Award, and the 2nd Annual American Eurocopter Vision Zero Aviation Safety Award, for research.
Witnesses’ Biographies

Late addition (21:00, 02/03/09):
Dr. Blumen’s slide presentation is An Analysis of HEMS Accidents and Accident Rates
Free PDF from NTSB of what was a PowerPoint presentation by Dr. Blumen.

This does not include the ground EMS calculation, which suggests that it was an afterthought. The IOM data are in here, which suggests that a little more thought went into that. Too bad. These data are not comparable. Dr. Blumen should have recognized this incompatibility.
Some of the presentations of the speakers are available at the Agenda link above in footnote [1].

^ 3 To Err is Human: Building a Safer Medical System
IOM (Institute of Medicine) PDF Summary
This is available in several different forms. The National Academies Press page that contains all of the links is here.
The pdf links download the pdf, they do not open it directly.
Free PDF Summary . . . . . Free PDF Report In Brief
or read the book online for free


Win Ben Stein’s Mind – Roger Ebert Review

While on the subject of false scientific controversies and movie stars, or at least movies, I might as well throw in a movie review.

I have not read many impressive movie reviews. The current review of eXpelled deserves attention. Previously, my favorite review was of True Romance. It was short and to the point, the review, not the movie. I do not remember who wrote the review, or the exact wording, but this was essentially the review – The best way to describe this movie is to tell you that Dennis Hopper is in it and that he plays the most normal character in the movie.

I am not likely to ever see eXpelled. I had thought about it as blog fodder, but Roger Ebert has done a much better job than I could in his review, Win Ben Stein’s Mind. I am impressed with the job that Roger Ebert does in explaining the mathematical material that is misrepresented by Creationists. Roger Ebert’s Journal is not something I had read before, but it was linked at Respectful Insolence with Best review of Expelled! ever?

The cartoon at the end is excellent. If you do not read the piece, at least go to the review, scroll down to the end, and read the cartoon.

One criticism. Ebert points to a number, 99.975%, as the percentage of scientists who accept the theory of evolution as true, but he does not give any source for this information. I do not know how this number was obtained. I do not see what might have been done to limit responses to those well versed in the science of evolution. What is a scientist and why approach this as if all scientists are equal in answer questions about evolution? While the number is impressive, it would not be proof of anything, except agreement among scientists. He does state, in the comments, that this is not proof, but just suggests support for evolution.

Mule Breath also writes about this false scientific controversy in Flat Earth 101. I suspect that he is just getting warmed up with this post.

There is much to write about this scientific religious controversy, the financial crisis, global warming, and just the inability of people to understand the scale of really large numbers.