**Core Concept**
Myxoedema coma is a life-threatening complication of untreated or severe hypothyroidism, characterized by impaired mental status, hypothermia, and cardiovascular instability. The diagnosis of myxoedema coma relies heavily on laboratory tests that assess thyroid function.

**Why the Correct Answer is Right**
Thyroid-stimulating hormone (TSH) is the most reliable and sensitive test for confirming hypothyroidism, including myxoedema coma. TSH is produced by the pituitary gland and regulates the release of thyroid hormones (T3 and T4) from the thyroid gland. Elevated TSH levels indicate primary hypothyroidism, while low TSH levels suggest secondary or tertiary hypothyroidism. In myxoedema coma, TSH levels are typically elevated due to the lack of negative feedback from low thyroid hormone levels.

**Why Each Wrong Option is Incorrect**
**Option B:** Thyrotropine-releasing hormone (TRH) is a hormone produced by the hypothalamus that stimulates the release of TSH from the pituitary gland. While TRH levels may be elevated in secondary hypothyroidism, it is not a direct indicator of myxoedema coma and is not the test of choice.

**Option C:** Tri-iodothyronine (T3) is a thyroid hormone that plays a crucial role in regulating metabolism. While T3 levels are often low in hypothyroidism, they can be normal or even elevated in non-thyroidal illnesses, making them less reliable for diagnosing myxoedema coma.

**Option D:** Tetra-iodothyronine (T4) is another thyroid hormone that is often low in hypothyroidism. However, T4 levels can be normal or elevated in non-thyroidal illnesses, making it less reliable for diagnosing myxoedema coma.

**Clinical Pearl / High-Yield Fact**
In patients with myxoedema coma, it is essential to administer thyroid hormone replacement therapy promptly, as delayed treatment can lead to increased mortality. The initial dose of thyroid hormone should be administered intravenously, and the patient should be closely monitored for signs of improvement or worsening.

**✓ Correct Answer: A. Thyroid stimulating hormone (TSH)**