By Eyal Shahar at Brownstone dot org.
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Preamble
The natural home for this work is a biomedical journal. There is zero chance, however, that a paper would be accepted by any conventional journal. Why? Because the results are earthshaking, as stated in the title.
This post is technical, but the preamble is not. For the non-academic reader, the preamble will serve two purposes: 1) to share an interesting story about the evolution of this work; 2) to give a simple summary of what I found.
So, stay with me at least through this section.
Although I have over 200 scientific publications, only a few were truly innovative in the sense of a creative idea that led to an interesting discovery. Most were uninspiring, "normal" science. I often wondered how those rare cases were born, and in retrospect, it was never prolonged thinking. Rather, it was an unexplained spark, a moment when an idea came into my mind out of the blue, or some loose ends got connected. This work had something of both.
I never trusted the results of the Pfizer trial. That 95% effectiveness against a respiratory virus was too good to be true - unprecedented in the context of a viral respiratory infection. I could not tell, however, what might have gone wrong.
Working on a recent post, I concluded that the culprit must have been the ascertainment of cases. For whatever reason, many cases have been missed in the vaccine arm, and therefore, the original results cannot be trusted. Is there any other way to estimate the true effectiveness against symptomatic infection from the trial's data? "Probably not" is the expected answer.
Coincidentally, I discovered another document on the Pfizer trial, titled "Final Full Clinical Study Report." In that lengthy document, Pfizer included estimates of the effectiveness against asymptomatic infection, which were based on a blood test in all participants (anti-N antibodies).
Is there a way to estimate the effectiveness against symptomatic infection from the effectiveness against asymptomatic infection?
That was the spark: posing a question that linked two loose ends. Answering it was not too difficult. Simple computational work.
Every analysis is based on some premises or assumptions. Here, I needed two:
First, I assumed that the vaccine does not prevent an infection. It may only prevent symptoms when infected. This premise is widely accepted now, and I was able to demonstrate it indirectly in the trial's data.
My second assumption had to do with the split of infections between asymptomatic and symptomatic. There are data on the topic, including data I was able to extract from the trial.
The rest of the work was no more than a simple equation I borrowed from an old paper and a few rows on an Excel file, which I will show at the end.
I promised a spoiler:
Of over half a dozen different computations, one resulted in zero effectiveness, one in 50%, and all others - up to 25%. We should follow the majority: it was no more than 25%. And that's before waning…
Sources of Data
To combine data on asymptomatic infections and symptomatic infections, I needed to find a relevant time window in which both types of data were available. It was between dose 2 (administered 21 days after dose 1) and one month later, a period for which the reported effectiveness was between 90.5% and 94.8%.
There were two sources for the data: the famous paper in the New England Journal of Medicine and the Pfizer document I mentioned in the preamble, which was presumably submitted to the FDA. Below you will find screenshots of the data I used. Red rectangles were added.


Preliminary Analysis
The starting table is simple: the number of cases of symptomatic infection and asymptomatic infection in the two arms of the trial within one month after the second dose.

The numbers in the right column were transcribed from table 36 above. The number 4 is based on the graph, and the number 90 was estimated from the table below the graph: 21 cases in 7 days ...