Well they say 60% of people have sexual activity at the age of 18. But that's basically also their take on it. We need more studies on those factors.
I don't think controlling for infection makes sense. You'd just get the result, it's 95% effective if you're not infected. And maybe some if you are. Disregarding age and all other factors. That's how medication gets approved. But that's not what we're interested in so they specifically excluded those studies. What we want to know is, given you're a random person from the streets, you don't know if you have HPV or catch it tomorrow... What's your best option? That's why they're probing for other factors. If you already did a good test (which seems to be problematic) and know you're not infected, just get the shot, it's already proven to work, we don't need studies on that.