(Sudden deafness ended?) How can I better communicate -and did I find- a major (conclusion-flipping) statistical error in a recently published paper? I think I found a major (conclusion-flipping) statistical error in a paper in an AMA journal.  Did I?
If I messed up, I'd like to know how; I hope someone can point me in the direction of my errors.  If I messed up, I must have made at least two major errors, as I came to the same conclusion in two independent ways.  I communicated with the journal editor and corresponding author.
Here, you can find the paper and the correspondence.  I reproduce it below.
To try to make this question fully self-contained, I'll summarize the issue.
The authors calculate the background rate of sudden sensorineural hearing loss (SSNHL) per year and compare it to the rate of SSNHL over a three-week post-intervention period, and graph "Estimated incidence of SSNHL, per 100 000 per y".   Their conclusion is that the data indicates the intervention does not increase the incidence of SSNHL; a substantially and significant reduction is indicated.
They state that "We then estimated the incidence of SSNHL that occurred after vaccination on an annualized basis."  But this cannot be what they calculated.  It is incompatible with what they report is the data their research yielded.

*

*It’s an error to limit the possible adverse side effect window to 3 weeks post-vaccination (excluding adverse events outside that window) but then spread the remaining adverse events over a year to calculate risk on an annualized basis.". It’s unjustifiable. A reasonable start for comparison would be to compare risk over the 3 weeks to the annual (52-week) risk, scaled to 3 week period. So the correct finding, based on their research, appears to be no risk difference over a 3 week period of SSNHL between groups, (0.6-4.4 vs 0.3-4.1, n.s.).


*Their conclusion implies that the authors have discovered that the intervention reduced SSNHL by about 94%. Which would be a groundbreaking discovery if confirmed, and a there’s no plausible mechanism presented for such a miraculous treatment effect, more evidence of grave error. It does not pass this basic plausibility test.


*As I finished writing this up, I found further concerns, which I'll put in an answer. I put in chat: https://chat.stackexchange.com/rooms/18/ten-fold because preliminary.
[end summary]
Again, here, you can find the paper and the correspondence.  I reproduce it immediately below.
I wrote: (slightly modified)

Sirs:
I write in respect to *.
I may have found an error in this paper.  I'm thinking:  It’s an error to limit the possible
adverse side effect window to 3 weeks post-vaccination (excluding
adverse events outside that window) but then spread the remaining
adverse events over a year to calculate risk. It’s unjustifiable. A
reasonable start for comparison would be to compare risk over the 3
weeks to the annual (52-week) risk, scaled to 3 week period. So the
correct finding appears to be that risk in a 3 week period of SSNHL,
whether vaccinated or unvaccinated, is the same (0.6-4.4 vs 0.3-4.1,
n.s.). A closer look at adverse events within shorter periods after
vaccination would be an appropriate topic for further research.
Another way to see this error is to consider whether the original
results pass a basic plausibility test. They do not. If the results
shown in the figure accurately reflected Incidence Range / 100k of
SSNHL between the vaccinated and unvaccinated, then it would suggest
that the authors had discovered that vaccination reduced SSNHL by
about 94%. Which would be a groundbreaking discovery, and a there’s no
plausible mechanism presented for such a miraculous treatment effect,
this is more evidence of grave error.
*Formeister EJ, et. al.  JAMA Otolaryngol Head Neck Surg. 2021;147(7):674–676. doi:10.1001/jamaoto.2021.0869
-Matthew

Assuming I have, this won't my first time spotting a major error in a peer-reviewed publication. (I think that was in article High-fructose corn syrup causes characteristics of obesity in rats: Increase body weight, body fat and triglyceride levels (2010) in 2010. This HFCS, Bocarsly, Princeton paper was wildly popular in the lay press.)
Yet I received this non-response response (emphasis mine):

Matthew,
Thank you very much for your recent communication about the
paper w published in JAMA Otolaryngology ("Preliminary Analysis of
Association Between COVID-19 Vaccination and Sudden Hearing Loss Using
VAERS").  As a peer reviewed publication this manuscript was vetted in
a process that includes assessment and validation of hypotheses,
methodologies, and conclusions.  Readers and scientists can have faith
in the integrity of these robust processes.  We look forward to seeing
this important field expand and would encourage all interested
scientists to consider peer reviewed publication of their work in the
field. We would encourage a thoughtful re-read of the manuscript to
understand the methodology, and additional reading on the topics of
idiopathic sudden sensorineural hearing loss and principles of
epidemiology, for your understanding. Respectfully, Dr. Eric
Formeister, MD, MS on behalf of the authors.

--
If I messed up, I'd like to know ; I hope someone can point me in the direction of my error(s).
 A: 
I write in respect to *.
This study should be withdrawn.

I'm not going to wade through the material here to form a view on whether you are right or wrong in your identification of an error.  However, I will say that I don't think it's a good idea to start by requesting that the paper be withdrawn.  The first appropriate action here is to write to the authors, explain your concern with the paper, and see if they agree that there is a mistake in the paper.  They might agree with you (and then take appropriate action themselves, such as post errata or a withdrawal) or they might disagree and give you a counter-argument to your position, or they might just ignore you.  Whatever happens, you will then be in a position where you can decide whether you want to proceed further, and you will have made an initial attempt to clarify the matter and resolve it with the authors before proceeding to take action with the journal.
If you start out guns-blazing requesting withdrawal, and it turns out you are wrong, you are going to look like a bit of a goose.  Even if you are right, using this as your opening communique is not a very collegial approach.  It is best to assume that academics are generally competent people who act in good faith and are concerned about the correctness of their work --- in cases where you think a paper might need to be withdrawn, it is usual to start by raising concerns with the author to see if they agree that there is a problem or not.

Yet I received this non-response response...

Okay, so obviously they don't agree that there is an error, but they haven't said why.  In this case, I recommend re-reading the paper as they suggest, soliciting some other opinions on it (as you are doing), and if you still think there is an error you should write back to them and ask them if they can please explain why your position is incorrect.  The mere fact that the paper has been through peer review does not mean that you cannot raise concerns and seek withdrawal, so I agree that this is something of a "non-response response".
Hopefully, the matter can be resolved between you and the authors, but if this proves impossible, then you can certainly write back the the journal editor and seek for the journal to make a decision.
