This study will evaluate the safety and effectiveness of the leptin replacement therapy in treating lipoatrophy or lipodystrophy-a condition in which there is a total or partial loss of fat cells. Patients with lipodystrophy lack sufficient leptin, because this hormone is produced by fat cells. The leptin deficiency usually causes high blood lipid (fat) levels and insulin resistance that may lead to diabetes. Patients may have hormone imbalances, fertility problems, uncontrolled appetite, and liver disease due to fat accumulation.