The simple challenge for anyone who thinks that the CDC is just fine using only this signal analysis is to put the actual numbers in a spreadsheet and see.

Oh, don't know which vaccines are proper comparators? Run a sensitivity analysis.

Oh, VAERS is too clunky to make that easy? Yeah, it's a dinosaur, and propositions to modernize it get ignored.

My second article adds some additional discussion of why after age stratification the COVID-19 vaccines dominate the c and d parameters---at least for those who aren't children (possibly them too).

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I'm not a mathematician, but I have been analyzing the VAERS data weekly since February. My videos on this are on Bitchute. I did one back in June, 2021 comparing the reported deaths from CV vaccines to the reported deaths of ALL other vaccines going back 30 years. The graph is shocking. Here's the link: https://www.bitchute.com/video/cKTBa3okRs8L/

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Jul 27, 2021Liked by Mathew Crawford

Thank you for this vitally important analysis. Like kris alman said, I cannot follow the math, although I do get the drift LOL. I strongly urge you to preface and end these types of posts with a boiled down summary in non-geek language. Or even after each section. It would make the sharing of your content much more impactful.

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You raise some excellent points. I think there is a logic behind their method that you are missing, however. And that is the issue of "stimulated reporting," which refers to people reporting more adverse events due to increased awareness of the existence of VAERS and/or increased fear surrounding the COVID-19 vaccines due to media exposure of adverse events, awareness of the reporting system, mobilization by vaccine critics, etc.

So their logic is as follows: if the reporting for all events increases by approximately the same amount (say 20x to use your example), then that would be an indication of stimulated reporting, not a safety problem. The method they use to differentiate 'safety signals' from 'stimulated reporting' is if they find a different pattern of increases across different types of events and/or age groups.

Of course in that case they can't distinguish between a vaccine that increases all adverse events across the board vs. stimulated reporting, but then we'd want to ask how likely is it that a vaccine would increase all adverse events by a similar amount across the board?

Anyway, I have done an analysis following examples and guidelines published by the CDC and found a very strong and clear safety signal. You can find the report in pdf format here:


Feel free to contact me at the e-mail at the top of the report.

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Jul 28, 2021Liked by Mathew Crawford

If I'm understanding correctly, the way the CDC defines the variables A, B, C, D is such that the ONLY thing actually compared in the PRR equation is how often a vaccine is followed by a specific side effect A more frequently than it's followed by other side effects B?

So if vaccine X has 100x as many side effects as vaccine Y, but the different classes of side effects retain the same relative frequencies to each other, then X will obviously come across as equally safe as vaccine Y?

(It bewilders me that at this point, there are people who still think the CDC could possibly be some benevolent but confused entity. The CDC is not confused. They want you dead)

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Jul 28, 2021Liked by Mathew Crawford

Link to an immensely long video from the American Front-line Doctors group which has been speaking out against everything that is wrong with the 'covid narrative" since very early on in 2020. AFLDs advocated early use of HCQ and other immune boosting therapies which many of the original doctors were using in US hospitals (without CDC or FDA approval) 7 were getting amazingly good results with very few if any High risk or elderly patients dying. the AFLDS has grown immensely since that time with many more doctors joining them and several Solicitors. Simone Gold one of the founders is also a solicitor/Attorney. The AFLDS have also been approached by a CDC whistleblower who has stated that the CDC has been deliberately holding back on covid vaccine deaths by at least a factor of 600% as this whistleblower has made a sworn statement with evidence that the CDC has hidden at least one of the eleven reporting lines with 45,000 covid vaccine deaths recorded which should have been reported on VAERS. the AFLDS has launched legal action against the CDC over this fraud. as well as several other lawsuits in the US over related matters. as Dr Pam Popper is doing with her Stand up State law suits to have closed states, re-opened as Florida, Texas, and south Dakota and a few others as well as many countries which would not go against the constition to enact any of the BS covid mandates: the AFLDS has put out this long video which I've watched on 2x speed due to it's horrendous length but there is a wealth of information about what has happened in the US why it's medical tyranny, illegal unconstitutional etc and would be a great video to edit into seperate speakers as they all have such great information while most people won't bother watching the entire video even on 2x speed :-) https://live.aflds.org/

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Jul 27, 2021Liked by Mathew Crawford

Mathew, please get a twitter account so you can promote your analyses. That's how you get readers. I have seen multiple tweeted links to this particular analysis today, but the links need a focal point, namely a twitter presence for you. You need the amplification of all the links pointing back to your twitter account (and additionally because people can then find links to your other articles there).

The article was excellent. My takeaway is that the PRR method suppresses the statistical signal unless there is ONE particular class/type of Adverse Event (AE) that is much worse than other observed AEs. That is a real weakness of PRR. A diffused/diverse misclassification (a human weakness of the AE reporters) then also has an effect that buries signals.

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Jul 27, 2021Liked by Mathew Crawford

With this level of statistics far beyond my retirement pay grade, I got lost in your data crunching.

Here are a few articles that may be helpful in your critique:

A Comparative Study of Data Mining Algorithms used for Signal Detection in FDA AERS Database

J Young Pharm, 2018; 10(4): 444-449


Method: Most commonly used three data mining algorithms (DMAs) (Reporting Odds Ratio (ROR), Proportional Reporting Ratio (PRR) and Information Component (IC)) were selected and

applied retrospectively in USFDA Adverse Event Reporting System database to detect five confirmed Drug Event Combinations.

Result: Among the three data mining algorithms, Information Component was found to have a

maximum sensitivity (100%) followed by Reporting Odds Ratio (60%) and Proportional Reporting Ratio (40%)

Commonality of Drug-associated Adverse Events Detected by 4 Commonly Used Data Mining Algorithms


Associations with adverse events were analyzed for 16 unrelated drugs, using the proportional reporting ratio (PRR), reporting odds ratio (ROR), information component (IC), and empirical Bayes geometric mean (EBGM).

Improvement in the Analysis of Vaccine Adverse Event Reporting System Database

Lili ZhaoORCID Icon,Sunghun Lee,Rongxia Li,Edison Ong,Yongqun He &Gary Freed

Pages 303-310 | Received 06 Aug 2019, Accepted 20 Apr 2020, Accepted author version posted online: 05 May 2020, Published online: 08 Jun 2020


Here's a concerning adverse event:

Sudden Onset of Myelitis after COVID-19 Vaccination: An Under-Recognized Severe Rare Adverse Event


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Jul 29, 2021Liked by Mathew Crawford

Since you asked for commentary on the paper I sent it to a young Harvard educated mathematician whom I respect. His reply is lengthy, but basically comes down to wondering about data sources and about whether or not there are simultaneous datasets being accumulated somewhere else. My reply to him ( I am a physician not a mathematician) is equally lengthy, and as worried as your paper indicates you are, based upon what I know from having assiduously searched for reliable sources of information since spring of 2020. Is there a place where I might send you these comments if he agrees to my copying at least portions of his email?

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Jul 27, 2021Liked by Mathew Crawford

Thank you for this. When I found this document months ago and began sharing it I knew there was much off about it. There are many other things of concern In it including the fact that they are only looking for preexisting AEs from a list of AEs. Etc.

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Jul 27, 2021Liked by Mathew Crawford

Thank you again, Mathew. What an excellent analysis. I'm sending to the few people left in my life who are still open minded. I also recommend this excellent in-depth essay about the Covid vaccine, as another excellent piece to share with others who have otherized those who haven't succumbed to the vaccine.


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Aug 1, 2021Liked by Mathew Crawford

This is actually extremely serious and deserves a serious answer. I've been going over this and it is scary stuff. The only question I have is do they have some special way of classifying the AEs - some grouping such that the b term can't over take the a term to screw up the signal?

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Mar 11, 2022Liked by Mathew Crawford

I have noticed that there has not been a release, that I can find, in the Pfizer documents, on how many shots have been given in total in the US population. So there is no way to find out the percentage of people injured. To me, (with the caveat that I have not devoted days to looking for this number within the pfizer data dump) this indicates they are aware that the percentage, just the gross percentage, is not something they want to disclose.

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Aug 2, 2021Liked by Mathew Crawford

Good report and Ive tweeted. Thanks for the information and Ive now subscribed

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Hi Mathew. Here are comments from a fellow PhD Statistician.

Proportional Reporting Ratio (PRR).

"Consider what would happen if an extremely dangerous vaccine were introduced that resulted in 20 times as many AEs of all types as all the other vaccines to which it gets compared [...] The PRR remains invariant in the scaling of adverse events!"

Yes, this is true. It's also kind of beside the point. The PRR is designed to measure whether a specific adverse effect is more common for vaccine X compared to all other vaccines. It's not intended to detect whether vaccine X more often exhibits a specific adverse effect. That might seem strange, it relates to conditional probability which is something that a lot of people struggle with.

When he multiplies by 20 to simulate an "extremely dangerous vaccine", he is making two important mistakes.

First: He is conflating a more dangerous vaccine with one that is more commonly used. The table deals with raw counts, so a vaccine that is used more widely is more likely to generate more adverse effects, simply because it is used more. That's one reason, for instance, that men get in more accidents than women: Because they tend to drive more miles. To take this into account, we need to scale the results. So, the scale-invariance that the author is complaining about is a feature, not a bug. If it wasn't scale-invariant, then we'd be concluding that commonly used vaccines are "more dangerous" simply due to the fact that they are used more. That would be dumb.

Second: If a vaccine is presenting a serious adverse effect that is very common, then it's very unlikely to even make it to the point of being recorded in VAERS. The clinical trials are designed to suss out any frequent adverse effects. The vaccines which "pass" their phase 3 trial are already filtered to not have common adverse effects. So the author's thought experiment of increasing the rate of adverse effect by a factor of 20, 50, or 1000 (!!) is, while a marginally interesting thought experiment, really not talking about a plausible scenario. It'd be like talking about how unsafe it is for a automobiles to be powered by jet engines. Sure, it's technically possible, but it's just not something that we encounter on the roads.

In the paragraph or so above the example spreadsheet, he writes:

And if ratios among AEs change little between vaccines (like for an AE that is the result of the presence of the spike protein) due to correlation, the denominators will change in a manner that is highly similar to the proportional changes in the numerators!

His language here is a bit imprecise (ironic, given his bragging about math), but I think he's basically saying here: If the rate of each AE is approximately the same, then the PRR won't pick up a signal. This is a "WTF moment" because this is exactly the purpose of the PRR. It's designed to see if a particular AE has an outsized frequency in a particular vaccine compared to adverse events in general. He's complaining about the PRR measuring what it's designed to measure (completely beside the point of scale-invariance). It's like computing a median and saying "This is going to be in the middle of all the data points!" as if it's some shocking revelation.

When he says:

Certainly there are conditions that result in safety signals, but these are far at the extremes for the AEs that we most need to understand. [...] Do you kinda get the sense that the PRR function is designed to hide signals of unsafe vaccines, not to identify them?

He is -- again -- complaining about the fundamental premise of the PRR. Just because something has a slightly increased rate does not make it apocalyptic. And again, he seems to be ignoring that this is about relative proportions of AEs, not about baseline proportions of AEs. If there is a common enough, serious AE, it should be getting caught in the phase 3 trial, not in VAERS. With VAERS, we are implicitly talking about extremely rare adverse events.

Not only does the PRR need to get out of line for a safety signal to be generated, the use of 'and' instead of 'or' means that other additional criteria must also be satisfied before the CDC self-reports a safety signal!

This complaint falls flat. This is the criterion to suggest a signal based on PRR. Further on in the document, Section 2.5, they note that there are several sources by which a potential signal can be detected:

FDA empirical Bayesian data mining, through CDC PRR data mining, and through descriptive analysis

The author's article is talking about just one of these. The criticisms he raises about PRR may well be identified through the FDA method, or through "descriptive analysis" - i.e. making some tables. So the little examples he put together to say "OMG! Look how bad the PRR is at detection!" can be caught by an analyst just looking at summary tables. So his entire complaint about PRR is completely invalid, because the things he's complaining about are not being structurally ignored.

In fact, chi-squared statistics are not even supposed to be used on data that is likely to be correlated when causal. Presumption of a negative test result is not a reasonable test standard.

Based on what I can tell, the author is misunderstanding here. The CDC document does not say that they are using a Chi-square test, but a Chi-square statistic. The statistic can be used even if the assumptions of the chi-square test are violated. It would be, at that point, just a measure of the consistency or lack of consistency of the table. It's like calculating a mean, you can do that even if you don't assume a Normal distribution and use a t-test.

Even worse---given that numerous academics, including statisticians, reviewed this document, it is hard to believe that the scale invariance embedded in the definition of PRR, or the logic that includes meeting multiple criteria at the same time, went unnoticed.

Indeed! So if it's "random person with some unspecified mathematical training" arguing that PhD statisticians (edit: whose application area of expertise is precisely this) looked at the same thing and thought it was fine ... then maybe, just maybe, the random person isn't really getting the point or comprehending the whole picture.


PRR deals with relative rates, because otherwise we would conflate "dangerous" with "common".

This means the scale-invariance the author complains about is a good thing.

The PRR signal detection method is just one of several methods, which means the scale-invariance the author complains about is not hiding potential problems.

Several of the author's points require common side effects, which would likely be detected in a phase 3 trial and prevent approval of the vaccine.

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I'm a middling programmer and see flaws in this logic. The "and" is what will throw lower numbers. In addition to this problem, the CDC has very clearly stated that they are *not* gathering data on "breakthrough infections of COVID-19" that do NOT result in hospitalization or death as they claim this is not clinically significant. This is on their website. This is now a huge problem and why they must back track on the previously ditched mask guidance - they have no gathered reliable case data on the vaccinated cases that are spreading within the community, and thus there are no other viable options - and this is not even accounting for those that may be experiencing vaccine enhanced disease (ADE) or various mutations that have yet to be identified. It is irresponsible data and number skewing because they incorrectly presume that if "everybody just gets the vaccine" or more people get it, this disease can be eradicated which is now a statistical impossibility. It is a grave mistake (or evil, as you mentioned) which will cost many lives.

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