FHA (Functional Hypothalamic Amenorrhea)

The goal of this study is to determine whether romosozumab will improve bone density in girls and women with functional hypothalamic amenorrhea (cessation of the menstrual period due to intense exercise, stress, or an eating disorder) who have low bone density. Participants will be randomly assigned to receive romosozumab or placebo for 6 months. All participants will receive one IV infusion of zoledronate at the 6 month visit. All participants will also receive transdermal estradiol and cyclic progesterone. We will investigate whether participants who receive active romosozumab will demonstrate greater improvements in bone density at one year than those who receive placebo. We will also compare bone density over a year with healthy controls (girls and women of similar age who have regular menstrual periods).

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