The CDC says that it has data showing that people who have received the most recent bivalent Covid booster are at less of a risk for hospitalization.
These are not clinical trials. The CDC and FDA have not seen the need for those! They are statistical analyses of hospitalizations.
The first study was of seven health care systems. They showed that people who had the booster were up to 38% less likely to be hospitalized from Covid than those who had not. The study did not take into account previous Covid infections nor did it account for antibodies or death rates.
The second study was of older adults, 65 and up. They showed that this populations had up to 84% less likelihood of hospitalization with a Covid infection. Again, this did not account for previous Covid infection and was not able to account for death rates. Only hospitalization.