Transdermal Estrogen in Women With Anorexia Nervosa

Inclusion Criteria: 1. Female 2. 19-45 years of age 3. DSM-5 psychiatric criteria for anorexia nervosa 4. \<85% of ideal body weight as defined by the 1983 Metropolitan Life Insurance Height and Weight Tables 5. Amenorrhea 6. T-score of \< -1.0 at spine or hip Exclusion Criteria: 1. Diseases known to affect bone metabolism, including untreated thyroid dysfunction, vitamin D deficiency, Cushing's syndrome, diabetes mellitus or renal insufficiency (eGFR \< 60) 2. Personal history of venous or arterial clot 3. History of stroke or myocardial infarction 4. History of hypercoagulable disorder 5. Personal history or history of a first-degree relative with breast cancer 6. History of hereditary angioedema 7. Any medication known to affect bone metabolism, including systemic glucocorticoids within three months of the baseline visit, depot medroxyprogesterone within 6 months of the baseline visit, oral bisphosphonates within one year of the baseline visit or IV bisphosphonates within three years of the baseline visit 8. Bone fracture within the prior 12 months 9. Serum potassium \< 3.0 meq/L, serum ALT \> 3 times the upper limit of normal or Hemoglobin \< 10 g/dL 10. Fasting serum triglyceride level \> 150 mg/dL 11. Pregnant or breastfeeding (or desiring pregnancy within the next 18 months) 12. Active substance abuse 13. Elevated PTH level 14. 25-OH vitamin D level \< 20 ng/mL 15. Low phosphorus level