The original study that found that daily PrEP works was the iPrEX study, in which researchers investigated PrEP in cisgender men who have sex with men (MSM) and transgender women. The first results from the iPrEX study showed 44% effectiveness in stopping HIV transmissions. However, that number includes everyone who was offered PrEP because they were in the study. Some of those people took the Truvada every day as directed, while some people missed some (or a lot) of doses, and some people did not take the medication at all.
When researchers analyzed blood samples from people in the study, they were able to determine that those who took Truvada every day had their HIV risk reduced by 99%. Those who took Truvada only 4 times a week had their HIV risk reduced by 96%. For people who took the pills less than 7 days a week, Truvada was still highly effective at reducing HIV risk:
Note though that even this long answer still leaves out many details. There’s more information available here and here. See also the links at the bottom of the page for more information about how researchers came up with these numbers.
This analysis looked only at cisgender men and transgender women. Results in demonstration studies around the world have shown consistently good results. Among cisgender men and transgender women participating in these studies, there have been no instances of seroconversion among people taking Truvada as PrEP at least 4 times per week. However, available evidence suggests that 6 to 7 doses per week, i.e. daily PrEP with good adherence, is needed to fully protect cisgender women from acquiring HIV infection via vaginal sex. This may also be true for transgender men having front hole sex, but there is currently not enough data to be sure.
The original study that showed PrEP 2-1-1 to be effect was the IPERGAY study. The results from the IPERGAY study showed 86% effectiveness in stopping HIV transmissions. However, as with the iPrEX study for daily PrEP, this number included several individuals who stopped taking the medication during the study. Later analyses and a subsequent open-label study of PrEP 2-1-1 demonstrated 100% and 97% reductions in HIV incidence among men who took the medication as directed. This research shows that PrEP 2-1-1 works just as well as daily PrEP. As a result of this research, the World Health Organization (WHO) has fully endorsed PrEP 2-1-1.
IMPORTANT! PrEP 2-1-1 has been shown to work only in cisgender men and transgender women and only with Truvada (not Descovy). The research shows that PrEP 2-1-1 does not work in cisgender women.