**Core Concept:**
The question is asking about the most sensitive screening test for prostate cancer in a 50-year-old male with a positive family history of prostate cancer. Sensitivity refers to the ability of a test to correctly identify individuals with the disease. Prostate-specific antigen (PSA) test is a common screening test for prostate cancer.

**Why the Correct Answer is Right:**
The prostate-specific antigen (PSA) test is considered the most sensitive screening test for prostate cancer among the options given. PSA is a protein produced by the prostate gland and can increase in cases of prostate inflammation or cancer. Due to its high sensitivity, PSA testing can detect prostate cancer even at an early stage when the disease is still treatable.

**Why Each Wrong Option is Incorrect:**
A. Digital rectal examination (DRE): While DRE can detect prostate cancer by finding a palpable mass or enlarged prostate, it has low sensitivity and is not as effective as PSA testing.
B. Transrectal ultrasound (TRUS): TRUS is a diagnostic tool used for image guidance during prostate biopsies; it is not a screening test.
C. Prostate cancer antigen 3 (PCA3): PCA3 is a genetic marker that can be detected in urine and may indicate prostate cancer risk; it is not a standalone screening test.
D. Serum prostate-specific antigen (PSA) test: Although PSA is a screening test, it is not specific for prostate cancer, as it can also be elevated due to benign prostatic hyperplasia, urinary tract infection, or other causes.

**Clinical Pearl:**
While serum PSA testing is a sensitive screening test for prostate cancer, it has a significant drawback: a high PSA value can be caused by non-cancerous conditions as well. This limits its specificity. A combination of PSA testing and digital rectal examination (DRE) can increase the accuracy of prostate cancer detection, but it is essential to consider clinical context, patient history, and other risk factors when making a decision about prostate cancer screening.

**Correct Answer:**
The correct answer is option D: Serum prostate-specific antigen (PSA) test. The PSA test is the most sensitive screening test among the given options. However, it is essential to consider the patient's clinical context, family history, and age when deciding to perform PSA testing for prostate cancer screening.