**Core Concept**
Metastatic prostate carcinoma is a hormone-sensitive cancer that relies on androgens for growth and progression. The primary treatment goal is to reduce androgen levels or block androgen receptors to slow tumor growth.

**Why the Correct Answer is Right**
GnRH (Gonadotropin-releasing hormone) analogs work by initially stimulating the pituitary gland to release gonadotropins (LH and FSH), which in turn stimulate the testes to produce testosterone. However, with prolonged administration, GnRH analogs downregulate the pituitary gland, leading to decreased LH and FSH secretion and subsequently reduced testosterone production. This decrease in testosterone levels slows the growth of metastatic prostate cancer cells. GnRH analogs are effective in reducing testosterone levels by 80-90% within the first six months of treatment.

**Why Each Wrong Option is Incorrect**
**Option A:** Radiotherapy is primarily used for localized prostate cancer, not metastatic disease. While it may provide palliative relief for bone metastases, it's not a primary treatment for metastatic prostate carcinoma.

**Option B:** Estrogen therapy is not commonly used for treating metastatic prostate cancer. In fact, estrogen can stimulate prostate cancer growth. The primary treatment for metastatic prostate cancer involves androgen deprivation therapy, not estrogen therapy.

**Option D:** Radiotherapy with chemotherapy is not the standard initial treatment for metastatic prostate cancer. While chemotherapy may be used in advanced cases or as part of a clinical trial, GnRH analogs are the first-line treatment for hormone-sensitive metastatic prostate cancer.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that GnRH analogs can cause initial flare-up of prostate cancer symptoms due to the initial increase in testosterone levels before the downregulation of the pituitary gland. This flare-up can be managed with concurrent anti-androgen therapy, such as bicalutamide, to prevent worsening of symptoms.

**✓ Correct Answer: C. GnRH analogs**