Role of Estrogen on Skeletal Outcomes in FHA

The purpose of this study is to assess whether the natural form of estrogen (17-beta estradiol) given as a patch so that it is absorbed through your skin, is better at improving bone strength over 1 year than natural estrogen (17-beta estradiol) taken by mouth, or a synthetic form oestrogen (ethinyl estradiol) given as a patch that also provides birth control. Participants will: 1. Take estrogen for 1 year either (i) in its natural form as a patch twice a week (and progesterone by mouth for 12 days of each month), or (ii) in its natural form as a pill daily (and progesterone by mouth for 12 days of each month), or (iii) in a synthetic form as a birth control patch weekly for 3 weeks with 1 week off the patch. You will not be able to choose which form of estrogen you will receive as this will be assigned to you based on a pre-existing randomization sequence (like the flip of a coin) 2. Take provided calcium and vitamin D supplements 3. Attend 4 study visits over 12 months with two at the beginning and then every 6 months that include: * History and Physical Exams * Lab Work * Imaging studies * Questionnaires * Dietary recalls