Diagnostic tests I: sensitivity, specificity, PPV and NPV
Build the 2×2 table in thirty seconds, calculate all four test characteristics, and explain why the same test has a different PPV in general practice and in hospital.
Reviewed and kept current
Last editorial review: 28 September 2026 · Next scheduled refresh: March 2027.
Clinical vignette
Begin with the patient. Read the case, weigh the options, then work through the unit.
Mr C, aged 61, has had symptoms that led to a hypothetical rapid test for colorectal cancer. The result is positive. He is frightened. He asks: “Does this mean I have cancer?”
The test has been evaluated in 1,000 symptomatic patients. Colonoscopy found colorectal cancer in 50 of them. The test was positive in 45 of the patients with cancer and in 190 of those without cancer. The leaflet describes the test as “90% sensitive”.
Mr C wants a number. Which number answers his question?
Options to weigh
- Tell him that the test is 90% sensitive, so he very probably has cancer.
- Draw the 2×2 table and tell him what proportion of people with a positive result in the evaluation had cancer.
- Explain that a positive result is not a diagnosis, and that the evaluation confirmed cancer by colonoscopy.
- Explain that a negative result would have been far more reassuring than a positive result is alarming.
Reflect
How would you explain what a positive result means for Mr C, so that he understands his own chance of cancer, and what would you be careful not to say?
What this unit covers
Pocket-sized and self-contained: three AKT-style questions, the answers explained, an expanded discussion with hyperlinked guidance, a decision algorithm and a certificate.
By the end of this unit you will be able to
Five steps, in order
Answer first, then learn. Each section unlocks as you progress, and your progress is saved in this browser.
1Three single best answer questions
Commit to an answer for all three single best answer questions, then submit. Sections 2–4 open on submission; your certificate opens at 2/3 or better.
Question 1 of 3
A hypothetical rapid test for colorectal cancer is evaluated in 1,000 symptomatic patients, 50 of whom have colorectal cancer on colonoscopy. The test is positive in 45 of the patients with cancer and in 190 of those without cancer.
What is the positive predictive value of the test?
Question 2 of 3
The same test is then introduced for screening asymptomatic adults, in whom the prevalence of colorectal cancer is much lower. Its sensitivity and specificity are unchanged.
Which of the following is most likely to occur?
Question 3 of 3
A D-dimer assay has a sensitivity of 97% and a specificity of 40% for venous thromboembolism.
Which statement about this test is most accurate?
2Answers explained
Question 1
Correct answer B. 19.1%
Build the table: a = 45 (true +), b = 190 (false +), c = 5 (false −), d = 760 (true −).
The distractors are the other cells of the same table — the AKT deliberately offers them. Always write the table before calculating.
Question 2
Correct answer D. PPV will fall and NPV will rise
Sensitivity and specificity are properties of the test (assuming a similar spectrum of disease). Predictive values depend on prevalence: as prevalence falls, a positive result is more likely to be a false positive (PPV falls) and a negative result is even more likely to be correct (NPV rises).
This is why tests validated in secondary care disappoint in general practice, and why screening programmes generate many false positives.
Question 3
Correct answer C. A negative result in a patient with a low clinical probability makes VTE very unlikely
SnNout: a highly Sensitive test, when Negative, rules out. Because almost everyone with VTE tests positive, a negative result (in a patient with a low pre-test probability) makes VTE very unlikely — which is exactly how NICE NG158 uses D-dimer.
- Low specificity means many false positives, so a positive D-dimer does not confirm VTE (option A) and PPV is not 97% (option E).
- In a high-probability patient, even a negative D-dimer leaves meaningful residual risk, so imaging is needed.
SpPin — Specific test, Positive result, rules in.
3Expanded discussion, worked examples & guidance
1. Always draw the table the same way
| Disease present | Disease absent | Total | |
|---|---|---|---|
| Test positive | a true positive | b false positive | a+b |
| Test negative | c false negative | d true negative | c+d |
| Total | a+c | b+d | N |
Columns = test properties (sensitivity, specificity — stable). Rows = what the patient wants to know (“I tested positive; do I have it?” — PPV, NPV — vary with prevalence).
Try it · live calculator
2×2 diagnostic table calculator
2. Worked examples
Worked example 1 — from percentages (the commonest AKT format)
A test has sensitivity 80% and specificity 95%. It is used in 2,000 people, of whom 10% have the disease. Calculate the PPV.
- Diseased = 10% of 2,000 = 200; well = 1,800.
- True positives = 80% × 200 = 160; false negatives = 40.
- True negatives = 95% × 1,800 = 1,710; false positives = 90.
- PPV = 160 / (160 + 90) = 160/250.
Answer. PPV = 64%. NPV = 1,710/1,750 = 97.7%.
Worked example 2 — same test, lower prevalence
Now use the same test in 2,000 people with 1% prevalence.
- Diseased = 20; well = 1,980.
- TP = 16; FN = 4.
- TN = 95% × 1,980 = 1,881; FP = 99.
- PPV = 16/(16+99) = 16/115.
Answer. PPV falls from 64% to 13.9%; NPV rises to 99.8%. Same test, different population.
Worked example 3 — working backwards
“Of 400 patients with a positive test, 100 had the disease. Of 600 with a negative test, 30 had the disease.” Find the sensitivity.
- a = 100, b = 300, c = 30, d = 570.
- Sensitivity = a/(a+c) = 100/130.
Answer. Sensitivity = 76.9%; specificity = 570/870 = 65.5%.
3. Trade-offs and thresholds
Moving a test’s cut-off trades sensitivity against specificity. Lowering the FIT threshold detects more cancers (higher sensitivity) but produces more false positives (lower specificity) and more colonoscopies. A ROC curve plots sensitivity against 1 − specificity across cut-offs; the area under the curve (AUC) summarises overall discrimination (0.5 = coin toss; 1.0 = perfect).
4. Why this matters in UK general practice: NICE NG12
NICE’s suspected-cancer guideline (NG12) uses a positive predictive value of 3% for a symptom or sign in primary care as the threshold for recommending urgent investigation or referral in adults. That is a PPV, not a sensitivity: it asks, “Of patients presenting to a GP with this feature, what proportion turn out to have cancer?” Risk assessment tools (e.g. QCancer, Hamilton’s risk assessment tools) present the same idea as a personalised probability.
- “Proportion of people with the disease who test positive” = sensitivity; “proportion of people who test positive who have the disease” = PPV. Read the grammar slowly.
- The AKT often gives more data than you need. Fill in all four cells anyway; it catches arithmetic slips.
- Prevalence in the study population equals pre-test probability only if the study population resembles your patient.
References and further reading
Guidance checked at the last editorial review (28 September 2026). Always use the current version.
- RCGP — Data interpretation topics in the AKT (PDF)
- NICE NG12 — Suspected cancer: recognition and referral
- NICE NG158 — Venous thromboembolic diseases: diagnosis and management
- NICE DG56 — Quantitative FIT to guide colorectal cancer pathway referral in primary care
- Oxford CEBM — Diagnostic study appraisal worksheet
4Decision algorithm
Answering any 2×2 question in five steps
Start
Write the 2×2 grid: disease across the top, test down the side.
Decision
Are you given absolute numbers?
Action
Complete every cell and check that the totals add up.
Decision
Does the question ask about the test (people with or without disease)?
Decision
Has prevalence changed?
Outcome
Sanity check: SnNout (a negative on a sensitive test rules out) and SpPin (a positive on a specific test rules in).
Revision summary; apply clinical judgement and local pathways.
5Certificate of completion
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