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.