Leptin is a hormone secreted by fat cells under normal conditions and acts in the brain to regulate energy usage and hormone levels. Women with HA who do not have regular periods have low leptin levels and may also have other hormone abnormalities as well as loss of bone density (osteopenia or osteoporosis). This study will evaluate how leptin (a fat cell hormone that normally circulates in the blood) affects bone density, menstrual periods, hormone levels, bone metabolism (how bone forms and turns over), immune function (how well the body can fight infection), metabolic rate (how many calories are used at rest), and overall sense of well-being and appetite in women with HA (i.e. no regular menstrual periods due to low levels of pituitary hormones that regulate estrogen production from the ovary). It will also investigate whether leptin replacement can be used as an adjunct to the current standard of care for HA patients, i.e. OCPs.