Correct Answer: C. 90/100
Sensitivity is the ability of a screening test to correctly identify those WITH the disease. It is calculated as: Sensitivity = TP / (TP + FN), where TP = true positives and FN = false negatives. In this question, the gold standard identified 100 people with DM (the true disease prevalence). Of these 100, the screening test correctly identified 90 (true positives). Therefore, the screening test missed 10 people (false negatives = 100 − 90 = 10). Sensitivity = 90 / 100 = 0.90 or 90%. This means the screening test correctly identifies 90% of those who actually have DM. The denominator is always the gold standard total (those truly diseased), NOT the screening test total. This is the critical distinction in Indian epidemiology curricula (Park's Textbook) — sensitivity answers the clinical question: "If someone has the disease, what is the probability the test will be positive?" It is independent of disease prevalence and depends only on the test's ability to detect true disease.
Why the other options are wrong
A. 90/1000 — This calculates the positive predictive value (PPV) or screening yield, not sensitivity. The denominator uses the entire screened population instead of only those confirmed to have disease by the gold standard. This is a common NBE trap — students confuse the screening test result (90 positive out of 1000 screened) with the true disease prevalence (100 by gold standard). PPV answers 'If the test is positive, what is the probability of disease?' — a different question entirely. B. 100/110 — This incorrectly adds TP (90) and FN (10) in the denominator to get 100, then adds the screening test positives (90) to get 110 — a mathematically nonsensical formula. This appears to confuse sensitivity with some hybrid calculation. The denominator 110 has no epidemiological meaning. This is a distractor designed to catch students who mechanically add numbers without understanding the sensitivity formula. D. (90-10)/1000 — This subtracts false negatives (10) from true positives (90) to get 80, then divides by total screened population (1000), yielding 80/1000 = 0.08. This is incorrect on two counts: (1) sensitivity never involves subtraction of FN from TP, and (2) the denominator should be the gold standard total (100), not the screened population (1000). This option exploits confusion between sensitivity and specificity calculations.
High-Yield Facts
- Sensitivity = TP/(TP+FN) — uses only the gold standard-confirmed diseased population as denominator; answers 'test positive if disease present?'
- Specificity = TN/(TN+FP) — uses only the gold standard-confirmed non-diseased population; answers 'test negative if no disease?'
- Sensitivity is independent of disease prevalence — a 90% sensitive test remains 90% sensitive whether prevalence is 1% or 50%
- High sensitivity screening tests are used to rule OUT disease (SnNout rule) — low false-negative rate is critical in initial population screening
- Gold standard defines truth in epidemiology — denominator for sensitivity/specificity always comes from gold standard classification, never from screening test results
Mnemonics
SnNout & SpPin SnNout = high Sensitivity rules OUT disease (negative test excludes disease). SpPin = high Specificity rules IN disease (positive test confirms disease). Use when deciding whether a test is better for screening (needs high Sn) or confirmation (needs high Sp). DENOMINATOR RULE Sensitivity denominator = all diseased (TP+FN from gold standard). Specificity denominator = all non-diseased (TN+FP from gold standard). Always ask: 'Am I calculating among the diseased or non-diseased group?'
NBE Trap
NBE pairs "90 positive on screening" with "100 positive on gold standard" to lure students into using the screening test total (90/1000) as PPV, or into confusing the two populations. The trap is that students forget the gold standard redefines the true denominator — the screening test result (90 positive) is irrelevant to sensitivity calculation.
Clinical Pearl
In Indian diabetes screening programs (e.g., ICMR-INDIAB), a screening test with 90% sensitivity means that among 100 people with true diabetes (confirmed by fasting glucose or HbA1c), the screening test will catch 90 — missing 10 who need intervention. This is why high-sensitivity tests are preferred for initial population screening in resource-limited Indian settings, even if specificity is lower.
_Reference: Park's Textbook of Preventive and Social Medicine, Ch. 10 (Epidemiology of Chronic Diseases); Robbins & Cotran Pathologic Basis of Disease, Ch. 1 (Diagnostic Pathology)_