Any study attempting to show or imply causation needs to control for confounding variables; this is statistics 101. Usually you do this with an aptly named control group.
If you don't have that control, you're left with "either my results are meaningful or else (very likely) there is a confounding factor." Great, that's not very useful.
Neither of these studies did they control for who was exposed to the actual disease.
As far as I have found, the only experiments that did do this were completely unethical, and have not been repeated in modern western science: (that I know of)
The control group was exposed to the actual disease at the same rate than the treatment group. The idea is that both groups get almost the same treatment.
If the groups are big enough, you expect from statistic that both groups would have a similar number of ill people without treatment and a similar number and type of "sede effect"without treatment. So the difference can be atribute to the drug/vaccine, if statistically significant.
A study were all the participants are exposed on purpose to the disease is very difficult to justify, with or without control group. Perhaps a vaccine for a strain of cold, that is an illness with a very low rate of deadly complications?
Any study attempting to show or imply causation needs to control for confounding variables; this is statistics 101. Usually you do this with an aptly named control group.
If you don't have that control, you're left with "either my results are meaningful or else (very likely) there is a confounding factor." Great, that's not very useful.