Is it worth having a scalp biopsy to determine the cause of my thinning hair?

A scalp biopsy if taken from a representative area and examined under the microscope by a dermatopathologist who is knowledgable can be helpful if the diagnosis is not clear. Many hair loss diagnoses do not require a scalp biopsy but rather a careful review of the patient's history and careful examination of the scalp via dermoscopy. Biopsies are not always 100% and sometimes one needs to interpret the result to make sure it fits with the clinical diagnosis. In other parts of medicine, a biopsy is the 'final' answer - that is not true in hair medicine.A biopsy would show the number of hairs and if there is miniaturization (a feature of genetic hair loss) and whether there are other features like scarring and inflammation.

There are systemic issues that can cause hair loss that require  biopsy for definitive diagnosis.  If you show no clinical signs it is less likely, but if there is doubt it is not a bad idea.