Ian Fellows writes:
I [Fellows] just wrote up a little Bayesian analysis that I thought you might be interested in. Specifically, everyone seems fixated on the 90% effectiveness lower bound reported for the Pfizer vaccine, but the true efficacy is likely closer to 97%.
Please let me know if you see any errors. I’m basing it off of a press release, which is not ideal for scientific precision.
Here’s Fellows’s analysis:
Yesterday an announcement went out that the SARS-CoV-2 vaccine candidate developed by Pfizer and Biontech was determined to be effective during an interim analysis. This is fantastic news. Perhaps the best news of the year. It is however another example of science via press release. There is very limited information contained in the press release and one can only wonder why they couldn’t take the time to write up a two page report for the scientific community.
That said, we can draw some inferences from the release that may help put this in context. From the press release we know that a total of 94 COVID-19 cases were recorded. . . .
We do get two important quotes regarding efficacy.
“Vaccine candidate was found to be more than 90% effective in preventing COVID-19 in participants without evidence of prior SARS-CoV-2 infection in the first interim efficacy analysis
…
The case split between vaccinated individuals and those who received the placebo indicates a vaccine efficacy rate above 90%, at 7 days after the second dose.”
How should we interpret these? Was the observed rate of infection 90% lower in the treatment group, or are we to infer that the true (population parameter) efficacy is at least 90%? I [Fellows] would argue that the wording supports the later. . . . the most compatible statistical translation of their press release is that we are sure with 95% probability that the vaccine’s efficacy is greater than 90%. . . .
Assuming my interpretation is correct, let’s back out how many cases were in the treatment group. Conditional on the total number of infections, the number of infections in the treatment group is distributed binomially. We apply the beta prior to this posterior and then transform our inferences from the binomial proportion to vaccine effectiveness. . . .
There is a lot we don’t know, and hopefully we will get more scientific clarity in the coming weeks. As it stands now, it seems like this vaccine has efficacy way above my baseline expectations, perhaps even in the 97% range or higher.
I [Fellows] could be wrong in my interpretation of the press release, and they are in fact talking about the sample effectiveness rather than the true effectiveness. In that case, 8 of the 94 cases would have been in the treatment group, and the interval for the true effectiveness would be between 81.6% and 95.6%. . . .
It is important to have realistic expectations though. Efficacy is not the only metric that is important in determining how useful the vaccine is. Due to the fact that the study population has only been followed for months, we do not know how long the vaccine provides protection for. There is significant evidence of COVID-19 reinfection, so the expectation is that a vaccine will not provide permanent immunity. If the length of immunity is very short (e.g. 3 months), then it won’t be the silver bullet we are looking for. I’d be happy to see a year of immunity and ecstatic if it lasts two. . . .
I’ve not tried to reconstruct this analysis, but I’m a fan of the general idea of trying to reverse-engineer data from published reports. We had a fun example of this a few months ago.
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