Some clinical trials are time-driven, such as chemo-therapy where you want to see how long it works.

The efficacy part of vaccine trials are event-driven... once you get X number of infections in the control group you're good. You just compare that to Y number of infections in the vaccine group to get your efficacy.

The number you need for X is actually pretty low, about 100 will do and the size of the trial group is irrelevant. 100 infections in the control, and 98 infections in the vaccine group is an efficacy fail. 100 control, and 4 vaccine is a resounding success.

Running very large trails (30-60K in the case of covid) does two things. First, it gets your control infections sooner. You *could* do a control group of 100 people, but you'd need to wait for ALL of them to get covid to get your number... despite all the media hype covid is still not that common. You could also hypothetically do a very small "challenge" trial, where you would deliberately expose to covid 100 each placebo and vaccine recipients... obvious ethical issues, but it's been done with non-lethal bugs before. J&J initially sized their stage 3 trial at 60K, but reduced it because of the covid surge... didn't need that many people to get timely results since covid is now more readily "available" than when they planned the trials last summer.

That's efficacy. Trail size is based on pathogen prevalence & contagiousness, and how quickly you need to get X infections in the control group. In the case of covid they wanted the data asap. You can certify the vaccine if efficacy and safety are good at that point.

Other aspects of trials are safety and duration of efficacy. A large trial group gives better confidence in safety. It also ensures that you'll have enough participants who stick with the monitoring programming long enough to get longer-term data on both efficacy duration and safety.