Frame PCOS by its dominant endocrine state: women do not ovulate regularly, so they make plenty of oestrogen from follicles but little or no progesterone. The result is high androgens and oestrogen that is never opposed by progesterone. Almost every long term complication of PCOS flows from this.
Continuous oestrogen without progesterone keeps the endometrium proliferating, which is exactly the setup for endometrial hyperplasia and cancer, so endometrial carcinoma belongs to PCOS. The syndrome is also a textbook cause of insulin resistance and the metabolic syndrome, and the high insulin feeds back to raise ovarian androgen output. A weaker but recognised link to ovarian carcinoma is also described.
Now look at osteoporosis. Bone loss of the osteoporotic type is driven by a lack of oestrogen, which is why it appears after menopause and in hypothalamic amenorrhoea. PCOS patients sit at the opposite end: their oestrogen is normal or high. With oestrogen present, the bone is protected, so osteoporosis is not part of the PCOS spectrum.
The item that does not fit is therefore osteoporosis.
\[\boxed{\text{Osteoporosis}}\]