Validity of a Screening Test: Sensitivity, Specificity and Predictive Values
The validity of a screening test is its ability to correctly distinguish people who have the target condition from those who do not. Validity is assessed by comparing the screening result with a trusted reference or gold standard.
Learning objectives
- Construct and interpret a 2 × 2 diagnostic table.
- Calculate sensitivity, specificity, positive predictive value and negative predictive value.
- Explain how disease prevalence affects predictive values.
- Distinguish validity from reliability and accuracy.
- Interpret cut-off points, ROC curves and likelihood ratios.
The 2 × 2 table
| Screening result | Disease present | Disease absent | Total |
|---|---|---|---|
| Positive | True positive (TP) | False positive (FP) | TP + FP |
| Negative | False negative (FN) | True negative (TN) | FN + TN |
| Total | TP + FN | FP + TN | N |
True positive
The test is positive and the condition is truly present.
False positive
The test is positive but the condition is absent.
False negative
The test is negative despite the condition being present.
True negative
The test is negative and the condition is absent.
Sensitivity
Sensitivity is the probability that a person with the disease tests positive. It measures how well the test finds disease.
Sensitivity = TP ÷ (TP + FN) × 100%
A highly sensitive test produces few false negatives. It is useful for initial screening when missing a case would be dangerous. A negative result from a highly sensitive test helps to rule out disease, provided the test is applied appropriately.
Specificity
Specificity is the probability that a person without the disease tests negative. It measures how well the test recognises non-disease.
Specificity = TN ÷ (TN + FP) × 100%
A highly specific test produces few false positives. It is valuable for confirmation when an incorrect positive result would cause harm, anxiety or costly treatment. A positive result from a highly specific test helps to rule in disease.
Predictive values
Positive predictive value (PPV)
The probability that a person truly has the disease given that the screening result is positive.
PPV = TP ÷ (TP + FP) × 100%
Negative predictive value (NPV)
The probability that a person truly does not have the disease given that the screening result is negative.
NPV = TN ÷ (TN + FN) × 100%
Key distinction
Sensitivity and specificity begin with the person's true disease status. Predictive values begin with the observed test result. Sensitivity and specificity are relatively stable properties of a test in a defined setting, while PPV and NPV change substantially with disease prevalence and population spectrum.
Worked example
A screening test is applied to 1,000 people. The reference standard shows that 100 have the disease. The screening test is positive in 90 of those 100 people and in 180 of the 900 disease-free people.
| Result | Disease + | Disease − | Total |
|---|---|---|---|
| Test + | 90 TP | 180 FP | 270 |
| Test − | 10 FN | 720 TN | 730 |
| Total | 100 | 900 | 1,000 |
- Sensitivity: 90 ÷ (90 + 10) = 90%.
- Specificity: 720 ÷ (720 + 180) = 80%.
- PPV: 90 ÷ (90 + 180) = 33.3%.
- NPV: 720 ÷ (720 + 10) = 98.6%.
- Prevalence: 100 ÷ 1,000 = 10%.
- Accuracy: (90 + 720) ÷ 1,000 = 81%.
Interpretation: the test detects 90% of diseased people and correctly gives a negative result to 80% of non-diseased people. However, only about one-third of positive results are true positives in this population, so diagnostic confirmation is essential.
Effect of prevalence
| When prevalence... | PPV | NPV | Practical meaning |
|---|---|---|---|
| Increases | Usually increases | Usually decreases | A positive result is more likely to represent true disease. |
| Decreases | Usually decreases | Usually increases | False positives form a larger share of all positive results. |
This is why a test may have the same sensitivity and specificity but very different predictive values when used in a high-risk clinic and in a low-prevalence general population.
Other measures
Accuracy
(TP + TN) ÷ N. The proportion of all results that are correct. It can be misleading when disease is rare.
False-positive rate
FP ÷ (FP + TN) = 1 − specificity.
False-negative rate
FN ÷ (TP + FN) = 1 − sensitivity.
Yield
The number of previously unrecognised cases detected by the programme.
Likelihood ratios
- Positive likelihood ratio (LR+) = sensitivity ÷ (1 − specificity). Larger values provide stronger evidence for disease.
- Negative likelihood ratio (LR−) = (1 − sensitivity) ÷ specificity. Smaller values provide stronger evidence against disease.
Likelihood ratios combine sensitivity and specificity and can be used with pre-test probability to estimate post-test probability.
Reliability versus validity
| Concept | Meaning | Question |
|---|---|---|
| Validity | Closeness to the true disease status | Is the result correct? |
| Reliability or precision | Consistency when repeated under similar conditions | Is the result reproducible? |
A test may be reliable but invalid if it repeatedly gives the same wrong value. Reliability is improved by standard procedures, calibrated equipment, training and observer agreement.
Cut-off points and ROC curves
Many tests use a numerical cut-off. Lowering the threshold generally increases sensitivity but decreases specificity; raising it generally increases specificity but decreases sensitivity. A receiver operating characteristic (ROC) curve plots sensitivity against the false-positive rate for different cut-offs. The area under the curve summarises discrimination: values closer to 1 indicate better separation of disease from non-disease.
Choosing a test
- Prefer high sensitivity when missing disease has serious consequences and an acceptable confirmatory test exists.
- Prefer high specificity when false positives lead to harmful, invasive or expensive action.
- Consider prevalence, feasibility, cost, acceptability, reliability and the entire follow-up pathway.
- Do not interpret a result without the clinical context and pre-test probability.
Common examination errors
- Using TP + FP as the denominator for sensitivity instead of PPV.
- Assuming a negative result always excludes disease.
- Claiming PPV is a fixed property independent of prevalence.
- Confusing reliability with validity.
- Calculating percentages before correctly labelling the 2 × 2 table.
Review questions
- Define sensitivity, specificity, PPV and NPV.
- Construct a 2 × 2 table and calculate all four measures.
- Explain how prevalence affects PPV and NPV.
- Distinguish validity, reliability and accuracy.
- Explain the trade-off created by changing a test cut-off.
- When should a highly sensitive or highly specific test be preferred?
References and further reading
- CDC Field Epidemiology Manual resources.
- WHO guidance on screening and diagnostic testing principles.
- Clinical Medicine Year 2 curriculum.
Educational use only. Test performance must be interpreted using validated local protocols, the target population and appropriate confirmatory testing.
