The sample size is big enough to get the error down to +/-.5%. That is, they are certain with 99% confidence that the actual value is between 94.5% and 95.5% for the Modern vax. If they doubled the sample size to 64K, it would only reduce the error to +/- .25% Being within half a percent is good enough.
Explanation of how statisticians calculate sample size ->
Yes, they could make the error on the calculation zero. However, they would have to count 100 million-plus cases instead of 32K. That is much more expensive and time-consuming and completely unnecessary. The slightly better result doesn't change what you learn from the calculation. 95.5% is basically the same result as 94.5% and that's the worst case. Most of the time it will be much closer to the result you would get if you count every case. I am only debating your assertion that the 32K sample is a red flag to fuckery. The actual study could be complete garbage. I don't know. However, they did have the good sense to use a sample size calculation that has been widely understood by scientists to be acceptable for hundreds of years.
"Why only 32867"
The sample size is big enough to get the error down to +/-.5%. That is, they are certain with 99% confidence that the actual value is between 94.5% and 95.5% for the Modern vax. If they doubled the sample size to 64K, it would only reduce the error to +/- .25% Being within half a percent is good enough.
Explanation of how statisticians calculate sample size ->
https://en.wikipedia.org/wiki/Sample_size_determination#Estimation_of_a_proportion
Yes, they could make the error on the calculation zero. However, they would have to count 100 million-plus cases instead of 32K. That is much more expensive and time-consuming and completely unnecessary. The slightly better result doesn't change what you learn from the calculation. 95.5% is basically the same result as 94.5% and that's the worst case. Most of the time it will be much closer to the result you would get if you count every case. I am only debating your assertion that the 32K sample is a red flag to fuckery. The actual study could be complete garbage. I don't know. However, they did have the good sense to use a sample size calculation that has been widely understood by scientists to be acceptable for hundreds of years.