Is this a serious academic paper?

A mathematical model for the determination of total area under glucose tolerance and other metabolic curves. (doi: 10.2337/diacare.17.2.152, Diabetes Care February 1994 vol. 17 no. 2 152-154)

From the abstract:

Yeah, it’s just the trapezoidal method of calculating an integral. Was this worthy of publication in a journal anyone takes seriously? In 1994?

This is basic calculus. People ought to have learned it in the first couple years of college, if not in high school. Also, what brain-dead ‘other formulas’ are diabetes researchers using? That last sentence in the part I quoted just deeply disturbs me and I doubt any explanation is going to allay my concerns.

I’d be very happy if someone explained to me what I’m missing here, because otherwise it seems like I should be able to get published in real journals by summarizing any half-decent calculus textbook.


What got this published was the idea that this particular model could be used for that particular health issue. Obviously the model is not rocket science, but since they tested other models it seems like it might be novel to apply this particular model to this particular problem. That, or the model had been used, but it hadn’t been conclusively shown to be better than the other models.

Academic papers can be pretty obvious stuff. I just wrote a well-received (but obviously not published) grad school paper statistically supporting the idea that sharing a border with a failed state is worse for rule of law than not. Obviously you and I know that being next to Somalia is going to be bad for your country. But until it’s published in a peer-reviewed journal, it doesn’t exist. If anyone ever wants to write “The border with Somolia has a negative effect on Kenya’s rule of law…” they are going to need to find a paper like mine to cite.

even sven: OK, I suppose that answers one of my questions.

The other, of course, is ‘Just how little calculus do diabetes researchers know?’, and I doubt we’ll get great answers to that without… an academic paper that someone will undoubtedly deride as really obvious.

It’s the Circle of Life!

Yep, it’s pretty bizarre. When I read the abstract I was sure it was a joke. But legit articles cite it. I would like to read the full article, but can’t seem to find it (even using a university proxy). Is it available (maybe I’m blind and missing the ‘full text’ link?

This is not my area of expertise, but it seems that the problem isn’t just that the authors potentially wrote a derivative paper, but that the reviewers accepted it.

It’s not just derivative. The abstract is very poorly written.

To see nearby libraries to you who own it in print, try WorldCat. Switch it to Articles search, limit it to the journal Diabetes care and then paste in the article title. It might ask you to put your zipcode in on the next screen.

Great site for finding library books.

WARNING: Mathematical joke follows:

How can it be derivative when it’s about integration?

Well, yes, of course it can be used for that particular health issue. That’s because the trapezoid method can be used for every such graph; it’s a general method for finding the area under a graph. This is literally high school mathematics. I remember doing this in Year 9.

The trapezoid method is mentioned in virtually every introduction to calculus. This paper shouldn’t have been published.

Not having read the article, I’m not really qualified to pass judgment, but here are some ideas.

First of all, the abstract does mention the accuracy of the trapezoid method against other methods. How would they be computing the error, if not by computing the “true” value with a definite integral? I hope they aren’t comparing it with experimental measurements (e.g. measure the patient’s blood sugar every five minutes and enter the number here).

I’m wondering if the paper may have a more pedagogical lean, in the sense of “Here is a technique that you can teach a minimally educated orderly to run, and it’s shown to be pretty accurate, so you can probably just go ahead and use it rather than waiting for someone who knows basic Calculus to come down and calculate the definite integral for you.”

And the trapezoid method isn’t really Calculus at all, it’s geometry, and something that I would expect any high school graduate to be able to do. Calculus says that you don’t have to approximate the area under the curve, you can compute it exactly.

In which state and/or country? In high school, (near Chicago, mid-1980s) we never got anywhere close to calculus or calculating areas under curves. At best, it may have been presented as “If you go to college, you can go on to learn calculus.”

My review of the medical literature indicates that the Tai model is employed by a variety of diabetic researchers as a way of rapidly figuring out variably timed responses to oral glucose loads.

As such, I think it just offers up a more convenient and yet clinically accurate formula for some niche clinical research folks who need a decent tool to solve the equation.

The fact that it was published in a diabetes care journal supports this interpretation.

Here’s another article suggesting a different way to generate the area under the curve as applies to glucose loads:

It mentions the Tai model, and notes its utility.

This is part of what specialty journals are for, to pass around helpful tips in the field of study. And allow for criticism of them, too.

You’re right, since you can’t do calculus on a function that you only know about through measurement at time intervals, particularly since the measurements have limited accuracy (as do all measurements of physical quantities). It’s numerical integration, which is a branch of numerical analysis – and it’s a pretty elementary algorithm for numerical integration.

But, in the end, is there a fundamental difference between a blood sugar curve and a probability density curve, or any other curve that you might want to compute the area under? I’d think that as long as you can show that a blood sugar curve is a curve of the type that you can compute the area under, you’ve just proven that any method for calculating the area underneath would work. Not rocket science, just brain surgery. It’s quite possibly the numerical analysis aspect, and the fact that this specific technique has been proven “good enough” for clinical use.

Exactly. Sometimes the insight is developing a new method, and sometimes it’s applying an old method to a new problem and packaging it in a way that non-specialists can understand. Any engineer or mathematician would know how to derive this formula, but they’re not the target audience for this article.

I graduated from a Catholic High School in Chicago in the early 90s and we did calculus either junior or senior year, both differentiation (calculating slope/rate of change) as well as integration (area under a curve.) It was an AP course, but it’s a standard high school AP course, from what I know.

There may be the difference - I wasn’t in any AP math classes.

But it seems a bit strange for anyone to regard this as a new problem, when it’s actually a very old one, known and solved centuries ago.

If I were to publish a paper describing how the temperature inside a brand new building can be measured with … a Thermometer!, what sort of reception could I expect?

At best this sort of thing seems to fall into the category of possibly useful tip.

A few years ago one of the students in my (molecular) department essentially derived the Binomial test. He gave a seminar showing how his “novel” method was much better than the methods that were currently used in his subfield and how he was getting ready to submit a methods paper describing it.

I took him aside and set him straight (and showed him how to do it in a much more formal and easier way). It WAS a better test than the current method (which wasn’t really a statistical test at all), but it didn’t warrant a separate paper - he just used it in his main paper with a paragraph describing the benefits.

While we are at it, let me throw in the reason I dropped out of math in sophomore High School in 1991- there was some incredibly easy basic algebra equation where you can always substitute zero for one of the values instead of going through some incredibly arcane steps to put zero in that value, and the teacher ridiculed me for it, I challenged her to disprove it, and she apologized, publicly, the next day.

I felt sorry for myself, her, and public education. I also failed to ever again attempt to memorize any formula given me, which has failed me many a time in life…