The most appropriate next step in management is to initiate levothyroxine therapy. This patient has subclinical hypothyroidism with a mild elevation of the serum thyroid-stimulating hormone (TSH) level and normal serum free thyroxine (T₄) level. Her family history of hypothyroidism and her thyroid peroxidase antibody positivity increase the likelihood of progression to overt thyroid failure. In patients with a mild serum TSH elevation (between the upper limit of normal and 10 µU/mL [10 mU/L]), beginning levothyroxine therapy is reasonable if symptoms suggestive of hypothyroidism are present.

Thyroid-stimulating immunoglobulins (TSIs) are highly associated with Graves disease. When the diagnosis of Graves disease cannot be made clinically in a patient with hyperthyroidism, measurement of the serum level of these antibodies is recommended, especially if radioactive iodine uptake studies are not available or if radioactive iodine exposure is contraindicated, as in pregnancy and breastfeeding. This patient does not have hyperthyroidism, and these tests are therefore not indicated.

Repeating a serum TSH measurement in this patient was reasonable, since up to 30% of patients with an initially abnormal serum TSH level will have a normalization of this value upon retesting. Since this patient has persistent elevation of TSH and symptoms that may be attributable to hypothyroidism, waiting 12 months before initiating therapy is not appropriate.

A radioactive iodine uptake (RAIU) scan is reserved for patients with hyperthyroidism. Patients with Graves disease typically have an elevated RAIU. Conversely, in patients with thyroiditis or exposure to exogenous thyroid hormone, the RAIU will be low (<5%) despite biochemical hyperthyroidism. Obtaining a thyroid RAIU in this patient is not indicated.