HPV infections can usually be cleared up by a healthy immune system, so there's a causal relationship with the immune system. There's a lot more information on it available here. [1] Risk factors for it managing to progress onto cancer include obviously the type of HPV infection and "immune status, the presence of other sexually transmitted infections, number of births, young age at first pregnancy, hormonal contraceptive use, and smoking."

I also wonder if 'number of births' is not largely a proxy instead for the shift in the immune system of a woman while pregnant; in effect they tend to become slightly immunocompromised, probably as a means of preventing an immune response from harming the baby.

[1] - https://www.who.int/news-room/fact-sheets/detail/cervical-ca...