Rapid antigen tests at the door reduce risk by about 75%, assuming people are asymptomatic and you test each day if it's a multi-day event. I did a deep dive on antigen tests recently, if you'd like to see the data.
PCR is probably similar: they're much more accurate, but the data is more stale, which especially with Delta is a significant issue.
The main post of what amounts of evidence different tests give is this one: https://www.lesswrong.com/posts/cEohkb9mqbc3JwSLW/how-much-should-you-update-on-a-covid-test-result
Also related is part of this post from Zvi (specifically the section starting “Michael Mena”): https://www.lesswrong.com/posts/CoZitvxi2ru9ehypC/covid-9-9-passing-the-peak
Combining the information from the two, it seems like insofar as you care about infectivity rather than the person having dead virus RNA still in their body, the actual amount of evidence from rapid antigen tests will be higher than the amounts given in the first post. There’s a good case to be made that the sensitivity with respect to infectiousness would be 95% or more, though I am not aware of any research directly addressing this question.
You can link to specific parts of posts, and thanks to the devs, it should now also show that part in the hover preview.
Or with a hyperlink.
Use the table of contents to get the link.
Suppose I am running a several-hundred-person indoor event in the US where all attendees are required to be fully vaccinated. Suppose also that no one will come to the event if they have COVID-like symptoms. Given full vaccination and lack of symptoms, how much additional risk reduction is there from requiring people to get a negative rapid test result at the door? Also, same question, but for requiring a negative result on a PCR test <48 hours before the event.
(I did not make an effort to look into this myself because I figured someone here would already know the answer, which would be way faster than me trying to figure it out from scratch. Please someone just tell me, thank you.)