Can anyone who is knowledgable about statistics answer this?

[PuzzledObserver]

One of the unanswered questions about the vaccines is whether they prevent transmission of the virus, or only stop vaccinated people from getting ill.

Once there are a lot of vaccinated people out there, will it be possible to tell from the data whether the vaccines are actually preventing (or reducing) transmission?

It seems self evident that a vaccine that reduces infection will reduce transmission. If there is no replication in vivo how are you going to get large quantities of virus in the respiratory tract?
mobile.twitter.com/andrew_croxford/status/1339156242032447489

will it be possible to tell from the data whether the vaccines are actually preventing (or reducing) transmission?

Yes. Some huge study will appear in The Lancet that is quasi-experimental in design (or whatever long winded way there is of describing study this design that Reviewer2 prefers).

In terms of mechanisms, it doesn't make sense that the vaccine would dramatically reduce sickness but not reduce viral shedding at all. I can't think of a vaccine that works like that.

I was pondering whether you could show lack of transmission with a case-control design - probably not, but I may be unreliable source. It's 9pm on a Friday when my brain is telling me Transformers is a good flick so I know I'm not firing on all cylinders.

Does anyone know if an antibody test would indicate who the 5% are for whom it didn't work. For example, if my uncle gets the vaccine and wants to get out and see his grandchildren regularly, is there a test which would show if the vaccine worked for him? I'm guessing not, as antibodies may not show up, or the tests are unreliable.