To the contrary, they do it all the time, e.g. silicone breast implants not responible for mixed contective tissue disease, vaccination with thimerosal preserved vaccines not responsible for autism, etc.
What Does the Institute of Medicine Report Say About the Safety of Silicone Breast Implants?
When they do statistical meta-analyses, they are not responsible for the original studies, some of which they eliminate for being problematic.
You are of course correct that statistical analysis is used in medical protocols and studies. Mea culpa ...