Which risk factor is associated with increased likelihood of developing osteoporosis?

The presence of delayed menarche is associated with an increased likelihood of developing osteoporosis, especially in females. Delayed menarche indicates a later onset of menstruation, which can lead to a prolonged period of low estrogen levels during the crucial years of bone density development. Estrogen plays a critical role in bone health; it helps maintain bone density by inhibiting bone resorption and promoting bone formation. When menstruation starts later than average, it may result in a slower accumulation of bone mass during the adolescent years, ultimately increasing the risk of osteoporosis later in life.

In contrast, the other options such as obesity, age at menarche, and family history have less direct and clear connections with the development of osteoporosis. Obesity can sometimes protect against osteoporosis due to higher bone density from increased mechanical loading on bones, while age at menarche and family history do play roles, but their influences are not as definitive as the effects of delayed menarche on estrogen levels and bone health during critical growth periods.