Screening tests
Screening Tests: Sensitivity, Specificity, PPV, NPV and Likelihood Ratios
How to calculate sensitivity, specificity, PPV, NPV, accuracy and likelihood ratios from a 2 × 2 table, and why predictive values change with prevalence. Also covers screening criteria, series and parallel testing, ROC curves, yield and common screening programmes.
One of the most tested topics in past papers
What screening is
- Screening applies a test to apparently healthy people to find unrecognised disease or risk at an early stage, when treatment works better. Its objective is early detection in well people, not diagnosis.
- A screening test sorts people into probably affected and probably unaffected; positives must be confirmed by a diagnostic test. Cervical screening (cytology or HPV testing) aims to find precancerous change in well women before cancer develops.
- Yield is the amount of previously unrecognised disease that is found and brought to treatment by screening. It rises with prevalence (screening high-risk groups), test sensitivity and follow-up of positives.
The 2 × 2 table for a test
| Disease present | Disease absent | |
|---|---|---|
| Test positive | a: true positive (TP) | b: false positive (FP) |
| Test negative | c: false negative (FN) | d: true negative (TN) |
- Read down the columns for sensitivity and specificity (start from true disease status); read across the rows for predictive values (start from the test result).
| Measure | Formula | Question it answers |
|---|---|---|
| Sensitivity | TP ÷ (TP + FN) = a/(a + c) | Of those with disease, what share test positive? |
| Specificity | TN ÷ (TN + FP) = d/(b + d) | Of those without disease, what share test negative? |
| PPV | TP ÷ (TP + FP) = a/(a + b) | If positive, how likely is disease? |
| NPV | TN ÷ (TN + FN) = d/(c + d) | If negative, how likely is no disease? |
| False negative rate | 1 − sensitivity | Share of the diseased missed |
| False positive rate | 1 − specificity | Share of the healthy wrongly flagged |
| Accuracy | (TP + TN) ÷ total | Overall share classified correctly |
| LR+ | sensitivity ÷ (1 − specificity) | How much a positive result raises the odds |
| LR− | (1 − sensitivity) ÷ specificity | How much a negative result lowers the odds |
Exam trap For NPV the denominator is everyone who tested negative (TN + FN); for specificity it is everyone without disease (TN + FP). Mixing these up is the commonest error.
Worked calculations
- PPV: 90 TP, 10 FN, 30 FP, 170 TN. PPV = 90 ÷ (90 + 30) = 75%. Sensitivity = 90 ÷ 100 = 90%; specificity = 170 ÷ 200 = 85%.
- NPV: 80 TP, 20 FN, 40 FP, 360 TN. NPV = 360 ÷ (360 + 20) = 360 ÷ 380 = about 95%. Sensitivity = 80%; specificity = 90%.
- NPV from negatives only: negative in 270 people without disease and 10 with it. NPV = 270 ÷ 280 = about 96%.
- Missed cases: sensitivity 80% in 200 diseased people means 160 detected and 40 missed (false negatives).
- Accuracy: 90 TP, 10 FN, 50 FP, 850 TN. Accuracy = (90 + 850) ÷ 1,000 = 94%.
- Effect of prevalence: 1,000 people, prevalence 10%, sensitivity and specificity 90%: TP 90, FN 10, FP 90, TN 810. PPV = 90 ÷ 180 = 50%; NPV = 810 ÷ 820 = 98.8%. At 1% prevalence, PPV falls to about 8%.
Properties of the test versus the population
- Sensitivity and specificity belong to the test and do not change with prevalence.
- Predictive values depend on prevalence: as disease becomes more common, PPV rises and NPV falls. In a low-prevalence population even a good test gives mostly false positives.
- Likelihood ratios are also independent of prevalence; post-test odds = pre-test odds × LR. LR+ over 10 strongly rules in; LR− under 0.1 strongly rules out.
- SnNout: a highly sensitive test, when negative, rules disease out (few false negatives), so it suits screening. SpPin: a highly specific test, when positive, rules disease in, so it suits confirmation.
- D-dimer is a sensitive but non-specific test. In a patient with low clinical (pre-test) probability, a negative D-dimer safely excludes DVT or PE because the NPV is very high. A positive result needs imaging; in high-probability patients go straight to imaging.
Remember Prevalence moves predictive values; it never moves sensitivity or specificity.
Cut-offs, ROC curves and combined tests
- Lowering the cut-off for a positive result catches more cases (sensitivity up) but flags more healthy people (specificity down), and vice versa.
- ROC curve: sensitivity against 1 − specificity across cut-offs. Area under the curve 0.5 is useless and 1.0 perfect; the point nearest the top-left corner balances both.
- Series testing (second test only if the first is positive, both must be positive): raises specificity and PPV, as in HIV screening with ELISA then a confirmatory test.
- Parallel testing (positive if any test is positive): raises sensitivity and NPV, used when missing disease is dangerous.
- Antenatal triple test for Down syndrome measures AFP, hCG and unconjugated oestriol (the quadruple test adds inhibin A). In Down syndrome AFP and oestriol are low, hCG and inhibin high.
- The most sensitive screening test for SLE is ANA (positive in about 95%); anti-dsDNA and anti-Sm are more specific.
Criteria for a screening programme (Wilson–Jungner, WHO)
- The condition is an important health problem.
- Its natural history is understood, with a recognisable latent or early symptomatic stage.
- A suitable, acceptable test exists: safe, simple, valid, reliable and cheap.
- Effective treatment exists and is better when given early.
- Facilities for diagnosis and treatment are available, and there is an agreed policy on whom to treat.
- The cost of case-finding is balanced against overall health spending (cost-effective), and case-finding is continuous, not a one-off.
Types, examples and harms
- Mass (population) screening of whole groups; targeted (high-risk) screening; opportunistic case-finding when patients attend; multiphasic (several tests at once).
- Examples: newborn heel prick (PKU, hypothyroidism, sickle cell, CF), newborn hearing (otoacoustic emissions), antenatal HIV, hepatitis B, syphilis, anaemia and thalassaemia, cervical (HPV or cytology), breast (mammography), bowel (FIT, colonoscopy), abdominal aortic aneurysm ultrasound in older men, diabetic eye screening, blood pressure.
- Harms: false reassurance (false negatives), anxiety and unnecessary tests (false positives), overdiagnosis and overtreatment, radiation, cost.
- Screening must be judged by RCTs with mortality as the outcome, because lead-time, length-time and volunteer biases all make screening look better than it is.
| Use | Test property wanted | Reason |
|---|---|---|
| Screening a population | High sensitivity | Miss as few cases as possible |
| Confirming a diagnosis | High specificity | Avoid labelling healthy people |
| Ruling out in low-risk patients | High NPV (sensitive test) | Negative result is reassuring |
How FCPS asks about this
- PPV from 90 TP and 30 FP: 90 ÷ 120 = 75%.
- NPV from 360 TN and 20 FN: 360 ÷ 380 = about 95%.
- Effect of rising prevalence on PPV: PPV increases; sensitivity and specificity unchanged.
- Cases missed by an 80% sensitive test among 200 diseased: 40.
- Accuracy with 90 TP and 850 TN out of 1,000: 94%.
- Negative D-dimer with low clinical probability: DVT safely excluded (high NPV).
- Meaning of yield in screening: previously unknown disease found and brought to treatment.
Test yourself on this topic
5 of the 37 questions in our bank on this topic. Choose an answer to see why every option is right or wrong.
In screening, what does 'yield' mean?
Answer: New disease found and treated
Yield is the amount of previously unrecognised disease that is diagnosed and brought to treatment because of screening. It depends on the sensitivity of the test, the prevalence of unrecognised disease, multiphasic screening (several tests at once), the frequency of screening, and participation of the public. Selecting high-risk groups (selective screening) raises the yield.
Yield of screening
- = new disease found and treated
- Raised by sensitivity, prevalence, high-risk targeting
- Also participation and multiphasic tests
Remember Yield is the harvest.
Why the other options are wrong
- Proportion who attend That is coverage or participation.
- Cost per case detected Cost-effectiveness.
- True positives among positives That is the PPV.
- Number of tests performed Not yield.
A woman with a low clinical probability of DVT has a negative D-dimer. What does this result allow?
Answer: DVT is safely excluded
D-dimer is a degradation product of cross-linked fibrin, so it rises whenever clot forms and breaks down. It is highly sensitive but poorly specific (raised in pregnancy, surgery, infection, cancer, old age, inflammation). Therefore a negative D-dimer in a patient with low pre-test probability (Wells score) reliably excludes DVT or PE (SnNOut), while a positive result needs imaging (compression ultrasound, CTPA). In high-probability patients, image directly.
D-dimer
- Fibrin breakdown product
- Sensitive, not specific
- Low probability + negative → exclude
- Positive → imaging
Remember D-dimer rules out, never rules in.
Why the other options are wrong
- DVT is confirmed A negative result cannot confirm disease.
- Imaging is still mandatory It has poor specificity.
- She must be anticoagulated Not indicated.
- Repeat it daily for a week Not needed.
A 50-g glucose challenge test is evaluated in an antenatal clinic. Of 120 women later confirmed by OGTT to have gestational diabetes, 102 had a positive challenge test. What is the sensitivity of the challenge test?
Answer: 85%
Sensitivity is the proportion of people with the disease who test positive: true positives divided by all who have the disease. Here it is 102/120 = 85%. The remaining 15% are false negatives. Sensitivity is calculated only from the people who have the disease, so the number of women without diabetes is not needed.
Sensitivity
- TP ÷ (TP + FN)
- Uses only the diseased
- Here 102 ÷ 120 = 85%
- High sensitivity rules out (SnOut)
Remember Sensitivity looks only at those who have the disease.
Exam trap Sensitivity and false-negative rate always add up to 100%.
Why the other options are wrong
- 15% This is the false-negative rate.
- 102% A proportion cannot exceed 100%.
- 54% Not derived from these numbers.
- 98% Not derived from these numbers.
A screening programme finds cancers earlier, and survival from diagnosis appears longer, but the age at death is unchanged. What explains this?
Answer: Lead-time bias
Lead-time bias: earlier diagnosis adds time between detection and death without changing when death occurs, so survival looks longer. Length-time bias: screening preferentially detects slow-growing tumours. Proper evaluation uses mortality in randomised screening trials.
Screening biases
- Lead-time: earlier diagnosis, same death
- Length-time: slow tumours found more
- Overdiagnosis: harmless disease found
Remember Starting the clock earlier isn't living longer.
Why the other options are wrong
- Recall bias Case–control studies.
- Selection bias by randomisation Randomisation reduces selection bias.
- Hawthorne effect Behaviour change when observed.
- Confounding by smoking Not explained by confounding.
A screening test for a fetal condition has a sensitivity of 90% and a specificity of 95%. It is offered to 10,000 low-risk pregnant women in whom the condition has a prevalence of 1%. Approximately what is the positive predictive value of the test in this population?
Answer: About 15%
Of 10,000 women, 100 have the condition and 90 of them test positive (true positives). Of the 9,900 without it, 5% (495) test positive (false positives). The positive predictive value is 90 ÷ (90 + 495) = about 15%. Even a good test has a low PPV when the condition is rare, because false positives from the large healthy group outnumber the true positives.
PPV and prevalence
- TP = 90, FP = 495
- PPV = 90 ÷ 585 ≈ 15%
- Low prevalence: low PPV
- NPV stays very high
Remember Rare disease, many false alarms.
Exam trap Sensitivity and specificity do not tell a woman her chance of being affected after a positive result; PPV does.
Why the other options are wrong
- About 90% This is the sensitivity.
- About 95% This is the specificity.
- About 50% Would need a much higher prevalence.
- About 99% Close to the negative predictive value, not PPV.
Where this sits in the CPSP syllabus
- Paper 1: Epidemiology, Screening: sensitivity, specificity, predictive values, likelihood ratios