Prostate cancer prevention with babies

It was recently reported in the popular press that becoming a father was associated with a drop in testosterone level. It seems intuitive that it is not the act of fathering the child (9 months prior) that leads to this, but rather living with the baby / baby's mother that causes testosterone to fall. If so, this mechanism should apply to any other males in proximity such as older siblings of the baby, grandparents and uncles, or what have you. A putative evolutionary mechanism put forth for this (by Sarah Hrdy; see link) is that male aggression is associated with infant mortality; perhaps lower testosterone leads to less aggression?

Fascinating, but this is about cancer prevention. Higher levels of testosterone are associated with higher prostate cancer risk (a phenomenon which has been invoked to explain racial disparities in prostate cancer incidence). Just as repeated pregnancies and consequent lower estrogen levels confer protection against (estrogen-associated) breast cancer, one would predict that incidence of prostate cancer would go down as number of consecutive babies in the house goes up.

If true, the next thing is to determine how it happens. It might be behavioral - maybe the male needs to be in the presence of fussy baby to get lower testosterone. If pheromonal, the male could just share air/living space with baby and never see or hear it. If the latter, it presents the possibility that baby pheromones might be bottled and then used over the long term as a natural testosterone suppressant for prostate cancer prevention.