How does clinical trial efficacy work (simply put)?

Post date: 2020-12-02 13:05:54
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Confused about the data provided on the recent COVID studies, and why they mean vaccines were judged to be 95% effective

The Pfizer and Moderna press releases (Pfizer's linked here) provide three main pieces of data: the number of trial participants, the number of participants who contracted the virus, and the number of participants contracting the virus who were in the control group, receiving a placebo. (Apologies for any mistakes in terminology or anything else I'll be making here.)

So for Pfizer's trial, there were more than 43,000 participants, 170 of them contracting COVID, and 8 of them were in the vaccine group, meaning 162 were in the placebo group. 8/162 is ~5%.

The press releases don't say that this is why the vaccines are judged to be 95% effective, though papers like the Washington Post connect the dots. But how is this not the wrong way to judge effectiveness? Wouldn't the right way be to say 162 out of 16,200, e.g., taking the placebo contracted it, and that's 1%, and 8 of let's say 16,200 receiving the vaccine contracted it, and that's 5% of 1%, meaning the vaccine is 95% effective?
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