A 52-year-old man from Delhi undergoes screening for colorectal cancer using a new faecal occult blood test (FOBT). The test has a sensitivity of 85% and specificity of 90%. His result is positive. The pre-test probability of colorectal cancer in this asymptomatic screening population is 5%. What is the most appropriate next step in management?

Explanation

## Clinical Context A positive screening test in an asymptomatic patient requires confirmation with the gold-standard diagnostic test. Although the test has good sensitivity (85%) and specificity (90%), the **positive predictive value (PPV)** in a low-prevalence population (5% pre-test probability) is much lower than the specificity might suggest. ### Calculating Post-Test Probability **Positive Predictive Value (PPV)** = $\frac{TP}{TP+FP}$ Using Bayes' theorem with the given parameters: - Sensitivity = 85% (true positive rate) - Specificity = 90% (true negative rate) - Pre-test probability = 5% $$PPV = \frac{0.85 \times 0.05}{(0.85 \times 0.05) + (0.10 \times 0.95)} = \frac{0.0425}{0.0425 + 0.095} = \frac{0.0425}{0.1375} ≈ 31\%$$ **Key Point:** Even with a positive test, the post-test probability of colorectal cancer is only ~31%. This is because the disease is rare in the screening population (5% prevalence), and the false positive rate (1 - specificity = 10%) creates many false positives. ## Management Algorithm ```mermaid flowchart TD A[Positive FOBT in asymptomatic screening]:::outcome --> B{High suspicion for CRC?}:::decision B -->|Yes: Post-test prob >30%| C[Refer for colonoscopy]:::action B -->|No: Low prob| D[Repeat test or observe] C --> E[Gold standard confirmation]:::outcome E --> F{CRC confirmed?}:::decision F -->|Yes| G[Staging + treatment planning]:::action F -->|No| H[Reassure patient]:::outcome ``` **High-Yield:** In screening populations with low disease prevalence, a positive test on a moderately sensitive/specific test still carries a relatively low post-test probability. Colonoscopy is the gold standard for confirming colorectal pathology and allows simultaneous therapeutic intervention (polypectomy). **Clinical Pearl:** The positive predictive value is heavily influenced by disease prevalence. In low-prevalence populations, even "good" tests generate many false positives. This is why colonoscopy (sensitivity ~95%, specificity ~100%) is the confirmatory gold standard. ## Why Colonoscopy Is Next 1. **Diagnostic confirmation** — colonoscopy is the gold standard for colorectal pathology 2. **Therapeutic opportunity** — polyps can be removed during the same procedure 3. **Risk stratification** — findings guide further management and surveillance intervals 4. **Standard guideline** — all major colorectal cancer screening guidelines recommend colonoscopy for positive FOBT