**Core Concept:**
Medullary thyroid carcinoma (MTC) is a type of thyroid cancer that originates from parafollicular cells, also known as C cells, which produce calcitonin hormone. Calcitonin is a vital biomarker for MTC as its levels increase significantly in MTC patients.

**Why the Correct Answer is Right:**
The correct answer is **D** - Calcitonin measurement. The primary screening method for medullary thyroid carcinoma is measuring serum calcitonin levels. When the levels of calcitonin are elevated, it indicates the presence of MTC, as mentioned above. This test is crucial in diagnosing MTC, as it directly correlates with the activity of the tumor cells.

**Why Each Wrong Option is Incorrect:**
A. **Option A (Antibodies against calcitonin):** While antibodies against calcitonin can be used in the diagnosis of MTC, they are not the initial screening method due to their limited availability and cost.

B. **Option B (Imaging studies):** Although imaging studies like ultrasound, computed tomography (CT), or magnetic resonance imaging (MRI) can be used to localize the tumor and its extent, they are not suitable for screening purposes. The primary role of imaging studies is to determine the stage and extent of the disease after a positive screening test.

C. **Option C (Tg measurement):** Thyroid-stimulating hormone (TSH) is a key hormone that stimulates thyroid gland activity, including thyroid-stimulating immunoglobulin (TSI) production. However, TSH and Tg levels are not reliable biomarkers for MTC screening. TSH is more commonly associated with differentiated thyroid carcinoma, and Tg is associated with papillary and follicular thyroid carcinoma.

**Clinical Pearl:**

In routine clinical practice, for the initial screening of MTC, measuring serum calcitonin levels is the preferred method due to its simplicity, cost-effectiveness, and high sensitivity in detecting early-stage MTC. Calcitonin measurement helps detect MTC even in its early stages, enabling prompt diagnosis and treatment, which is crucial for a better prognosis.

**Correct Answer: D (Calcitonin measurement)**