**Core Concept**
Iron deficiency is a condition characterized by a decrease in the total body iron stores, which can lead to various clinical manifestations. The earliest signs of iron deficiency are often subtle and can be attributed to the reduction in circulating iron available for erythropoiesis and other cellular functions.

**Why the Correct Answer is Right**
The correct answer is related to the earliest detectable change in iron deficiency. In iron deficiency, the circulating iron levels are reduced, which affects the production of hemoglobin and other iron-containing proteins. The earliest parameter to fall in iron deficiency is the serum ferritin level, which reflects the body's iron stores. A decrease in serum ferritin indicates a reduction in the total body iron stores, making it the earliest detectable change in iron deficiency.

**Why Each Wrong Option is Incorrect**
* **Option A:** Serum iron levels may also be affected in iron deficiency, but they are not the earliest parameter to fall. Serum iron levels can fluctuate due to various factors, making them less reliable as an early indicator of iron deficiency.
* **Option B:** Transferrin saturation is a measure of the percentage of transferrin that is saturated with iron. While it can be affected in iron deficiency, it is not the earliest parameter to fall. Transferrin saturation can be influenced by various factors, including inflammation and liver disease.
* **Option C:** Hemoglobin levels may decrease in severe iron deficiency, but they are not the earliest parameter to fall. Hemoglobin levels can be influenced by various factors, including anemia of chronic disease and other forms of anemia.

**Clinical Pearl / High-Yield Fact**
In iron deficiency, the earliest detectable change is a decrease in serum ferritin levels. This can be an important clue in diagnosing iron deficiency, especially in patients with mild or early symptoms.

**Correct Answer:** C.