This protocol is a randomized, double-blind, placebo-controlled clinical trial which aims to investigate the effect of romosozumab on BMD in women with anorexia nervosa. The investigators will also investigate the safety of romosozumab in women with anorexia nervosa. The investigators hypothesize that 12 months of romosozumab administration will result in an increase in bone mineral density, increase in markers of bone formation and decrease in markers of bone resorption, and improvement in bone microarchitecture in osteopenic women with anorexia nervosa compared with placebo.

In Phase 2, participants will receive a single infusion of open-label zoledronic acid (an intravenous bisphosphonate) 5 mg after the initial 12-month administration of romosozumab or placebo. The investigators hypothesize that 12 months of romosozumab followed by a single intravenous infusion of open-label zoledronic acid will result in a greater increase in BMD compared to 12 months of placebo followed by a single intravenous infusion of open-label zoledronic acid. Within the group of women who receive sequential therapy with 12 months of romosozumab followed by a single intravenous infusion of zoledronic acid, the investigators hypothesize BMD will be maintained between 12 and 24 months following administration of zoledronic acid.

Inclusion Criteria:

• Female
• Age 20-60 years, skeletally mature with closed epiphyses
• Body mass index (BMI) ≥ 16.5 kg/m2
• Anorexia nervosa or atypical anorexia nervosa defined by DSM-V diagnostic criteria
• BMD Z-score < -1.0
• Normal serum 25-OH vitamin D (>30 ng/mL) and calcium levels
• For women of reproductive age, agree to use an effective contraceptive method. Highly effective methods of birth control include: Combined (estrogen and progestogen) hormonal methods (pills, vaginal ring, or skin patch); Intrauterine device (IUD); Intrauterine hormonal-releasing system (IUS); Surgery to tie both fallopian tubes (bilateral tubal ligation/occlusion); Woman's male partner has had a vasectomy and testing shows there is no sperm in the semen
• Dental check-up within the past year

Exclusion Criteria:

• Hospitalization within 3 months of baseline study visit, including inpatient eating disorder treatment facility; participating in a residential eating disorder treatment program within 3 months of study participation is permitted
• Myocardial infarction or stroke within 1 year preceding enrollment
• History of hypertension or use of anti-hypertensive medications within the past 6 months
• Any disease known to affect bone, including untreated thyroid dysfunction, Cushing's or renal failure
• Any medication known to affect bone metabolism within 3 months of the study, excluding oral contraceptives or other forms of estrogen administration. Bisphosphonates must have been discontinued for at least one year before participation
• Immunodeficiency or taking immunosuppressive therapy
• Serum 25-OH vitamin D level <30 ng/mL
• Serum potassium <3.0 meq/L
• Serum magnesium <1.5 meq/L
• Serum ALT >3 times upper limit of normal
• eGFR of less than 30 ml/min
• LDL > 190 mg/dL
• Hypocalcemia
• Diabetes mellitus
• Active substance abuse, including alcohol
• Current smoker
• History of malignancy
• Paget disease of bone
• Osteomalacia
• Osteonecrosis of the jaw (ONJ) or risk factor for ONJ, such as invasive dental procedures (eg, tooth extraction, dental implants, oral surgery in the past 6 months), poor oral hygiene, periodontal and/or pre-existing dental disease, and current use of corticosteroids.
• Planned invasive dental procedure over the next 24 months
• Known sensitivity to any of the products or components of the medication to be administered
• Sensitivity to calcium or vitamin D supplements
• Pregnant, planning to become pregnant within 12 months after the end of treatment and/or breastfeeding
• Hypersensitivity to any component of zoledronic acid

Baseline to 12 months.

Double Blind