Actually you said:
"In all of the many studies conducted, there has yet to be a SINGLE serious adverse reaction."
What we have here is a failure to communicate. 4 people in the sample population died in car crashes during the course of the study. Are you seriously suggesting Gardasil causes car crashes? There were no serious adverse reactions to the drug. That's different from saying all 10,000 participants were in perfect health and none had any health problems. But no serious problems have been linked to Gardasil -- not one.