How do you approach the problem of TSH elevation in a patient on high-dose thyroid hormone replacement?

Persistent elevation of TSH levels in patients under treatment for hypothyroidism is a relatively common clinical problem in endocrinology practice. The most common cause for this phenomenon is poor patient compliance with their thyroid hormone tablets. In the compliant patient, however, multiple aetiologies are possible and a methodological and stepwise approach to the patient's problem will uniformly identify a cause, or at least a resolution.