BAKERSFIELD, Calif. -- Osteoporosis and breast cancer are two of the most common ailments affecting older women today, and there is a surprising paradox between the disorders.

Women with weak bones have a higher risk for osteoporosis but a lower chance of breast cancer.

While women with strong bones have a low risk for osteoporosis but a higher risk for breast cancer. Researchers suspected that the common connection is hormones, which help strengthen bones but can also spur cancer growth.

Doctors from the University of Arizona studied the relationship between bone density and breast cancer risk in nearly 10,000 postmenopausal women.

On average, each unit increase in high bone density raised the odds of breast cancer by 25 percent.

Those who had high bone density in addition to other risk factors -- such as older age, previous breast biopsies, or a family history of the disease -- roughly doubled their risk.

Experts suggested that women in the highest risk category may want to talk to their doctors to make sure they are being screened frequently enough for breast cancer.