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Medical researcher discovers integration, gets 75 citations (2007)

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Re: Medical researcher discovers integration, gets 75 citations (2007)

#21

Post by klingon78 »

learnstats2 wrote: post #15

The author of this blog post is wrong to say this is 'integration'[0], and is also later wrong to say it's the 'trapezoidal rule'[1]. It seems to me that it's diagnostically useful to have a standardised method for estimating the area under the curve, rather than everyone inventing their own method. [0](since you don't know the whole function, you only know point estimates at particular moments in time) [1] (trapezoi…

Is this something that could be applied in general mathematics? If so, is it truly novel and worthy or a trivial derivation? I’m asking because I don’t know, not rhetorically.

I agree that someone shouldn’t be publicly made fun of in-general for sharing something novel and non-trivial that others didn’t already know, and if it highlights a problem in inadequate reviews, maybe it should’ve been presented to the journals that published it with that info.

Re: Medical researcher discovers integration, gets 75 citations (2007)

#22

Post by vilhelm_s »

In the next issue, the journal published a bunch of letters noting that she had rediscovered the trapezoid rule.

https://kconrad.math.uconn.edu/math1132s20/handouts/taicomme...

Mary Tai herself also replied and explained the background to the paper a bit more:

> While a doctoral candidate working on my dissertation at Columbia University in 1981, I needed to calculate total area under a curve. During a session with my statistical advisor, and after examining several alternative methods, I worked out the model in front of him. The concept behind it is obviously common sense, and one does not have to consult the trapezoid rule to figure it out. [...]

> Why I call it Tai's model. I never thought of publishing the model as a great discovery or accomplishment; it was not published until 14 years later, in 1994. Because of its accuracy and easy application, many collegues at the Obesity Research Center of St Luke's-Roosvelt Hospital Center and Columbia University began using it and addressed it as "Tai's formula" to distinguish it from others. Later, because the investigators were unable to cite an unpublished work, I submitted it for publication at their request. Therefore, my name was rubber-stamped on the model before its publication. [...]

Re: Medical researcher discovers integration, gets 75 citations (2007)

#23

Post by ojnabieoot »

klingon78 wrote: post #21
learnstats2 wrote: post #15

The author of this blog post is wrong to say this is 'integration'[0], and is also later wrong to say it's the 'trapezoidal rule'[1]. It seems to me that it's diagnostically useful to have a standardised method for estimating the area under the curve, rather than everyone inventing their own method. [0](since you don't know the whole function, you only know point estimates at particular moments in time) [1] (trapezoi…

Is this something that could be applied in general mathematics? If so, is it truly novel and worthy or a trivial derivation? I’m asking because I don’t know, not rhetorically. I agree that someone shouldn’t be publicly made fun of in-general for sharing something novel and non-trivial that others didn’t already know, and if it highlights a problem in inadequate reviews, maybe it should’ve been presented to the journa…

I don’t think there’s anything here for mathematicians. The only nontrivial fact in the paper is that the approximation works well in medical practice (which is not something that Leibniz or Newton would have been able to tell you since there could be complicated biological factors confounding it - what if the ‘real curve’ has a bunch of spikes that don’t show up in measurements?).

However, the original paper really is incomplete because of its seeming ignorance of the real “trapezoidal rule.” It really needs a discussion along the lines of “the trapezoid rule from ordinary calculus can be used by diabetes practitioners with surprising accuracy” and explained that sources of error, discontinuity, etc., aren’t likely to affects the approximation.

But don’t worry about M.M. Tai’s feelings too much :) The paper is almost 30 years old and it’s world-famous for the silly error, Tai has already been throughly roasted.

Re: Medical researcher discovers integration, gets 75 citations (2007)

#24

Post by Niksko »

klingon78 wrote: post #21
learnstats2 wrote: post #15

The author of this blog post is wrong to say this is 'integration'[0], and is also later wrong to say it's the 'trapezoidal rule'[1]. It seems to me that it's diagnostically useful to have a standardised method for estimating the area under the curve, rather than everyone inventing their own method. [0](since you don't know the whole function, you only know point estimates at particular moments in time) [1] (trapezoi…

Is this something that could be applied in general mathematics? If so, is it truly novel and worthy or a trivial derivation? I’m asking because I don’t know, not rhetorically. I agree that someone shouldn’t be publicly made fun of in-general for sharing something novel and non-trivial that others didn’t already know, and if it highlights a problem in inadequate reviews, maybe it should’ve been presented to the journa…

This is kind of where grand parent's thesis (that the paper is in fact novel and useful) falls down.

I'd be stunned if the concept of integrating an unknown function that needs to be guessed based on measurements taken at irregular points in time hasn't been studied rigorously from a generalized mathematical point of view. What such study would likely do (that a medical treatment would not) is discuss tradeoffs of different approximation methods, probably explore things like error bounds and behaviours with different unknown functions, and selection of the best integration method.

GP is right in that I'm sure it's useful to have a standardized method that allows for comparison between doctors and patients. But I think it's naive to assume that the findings in this paper are mathematically novel, and further, that mathematicians couldn't do a more rigorous job of deducing an accurate 'standard' way of measuring this.

Re: Medical researcher discovers integration, gets 75 citations (2007)

#26

Post by stuartbman »

I think it's important to note why the 75 citations isn't just 75 dummies who also haven't heard of integration.

If you're writing a diabetes paper and want to use integration for your analysis (even if you are fully aware of its background), you'll be forced to justify your approach and defend it's applicability to diabetes. Far easier to say 'as per Tai et al...' and take it as given.

You see this a lot- 'we used [x] because Big Name Prof did as well [citation]'

Re: Medical researcher discovers integration, gets 75 citations (2007)

#27

Post by newswasboring »

vilhelm_s wrote: post #22

In the next issue, the journal published a bunch of letters noting that she had rediscovered the trapezoid rule. https://kconrad.math.uconn.edu/math1132s20/handouts/taicomme... Mary Tai herself also replied and explained the background to the paper a bit more: > While a doctoral candidate working on my dissertation at Columbia University in 1981, I needed to calculate total area under a curve. During a session with m…

I was really on the author's side till I read these responses. Initially in my head it was just a case of misunderstanding or ignorance, but through her letters she has made clear that she thinks it is significant enough. This is borne out by her tone which is palpatably aggressive and contradictory at some points. She says she didn't publish this model for glory, but she also named it after herself. Also, no effort was made to connect it to already known elementary mathematics. And I don't understand why people would need a citation instead of just saying its calculated using the trapezoidal rule. The whole point about model vs formula is IMO pathetic, models are not just bunch of known formulas. They are supposed to give a new understanding of the system (also who brings up Marriam Webbster in a medical journal? Even in letters it sounds incredibly condescending).

Re: Medical researcher discovers integration, gets 75 citations (2007)

#29

Post by hef19898 »

Niksko wrote: post #24
klingon78 wrote: post #21

Earlier quoted context omitted.

Is this something that could be applied in general mathematics? If so, is it truly novel and worthy or a trivial derivation? I’m asking because I don’t know, not rhetorically. I agree that someone shouldn’t be publicly made fun of in-general for sharing something novel and non-trivial that others didn’t already know, and if it highlights a problem in inadequate reviews, maybe it should’ve been presented to the journa…

This is kind of where grand parent's thesis (that the paper is in fact novel and useful) falls down. I'd be stunned if the concept of integrating an unknown function that needs to be guessed based on measurements taken at irregular points in time hasn't been studied rigorously from a generalized mathematical point of view. What such study would likely do (that a medical treatment would not) is discuss tradeoffs of di…

If you look close enough, you see this kind of thing quite often, eyperts in one field "discovering" the basics of another, non related, field. And then praising themselves for discovering it. No idea if people looked at that, but I sometimes have the impression, that our hyper specialization isn#t helping.

I see this at the moment a lot with supply chain management. Best example used to be masks, and no vacinations. It is kind of funny to see in real time people dicovering, and trying to cope with, the time axis coming with purchase orders, volumes and delivery dates. It is also quite saddening to watch. A medical researched discovering maths I learned already before entering university falls into kind of the same category.

Re: Medical researcher discovers integration, gets 75 citations (2007)

#30

Post by _v7gu »

diarrhea wrote: post #10
Cu3PO42 wrote: post #7

Amusingly this paper is cited in the "Failures" section of Wikipedia's article on "Scholarly peer review": https://en.wikipedia.org/?curid=33158412#cite_ref-Tai_1a_165...

How did you randomly dig that up? That's a somewhat hidden entry.

This link works too: https://en.wikipedia.org/wiki/Scholarly_peer_review#Failures
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