Screening Tests: Sensitivity & Specificity

Dr. Arun Mitra

Department of Community Medicine

2026-07-07

Question

A rapid HIV test used in an antenatal camp is 90% accurate.

Asha tests positive.

What is the chance she truly has HIV?

  • (a) about 90%

  • (b) about 50%

  • (c) less than 10%


Write the answer on a piece of paper. We will come back to this at the end.

Why screen at all?

Screening ≠ Diagnosis

Screening

  • Apparently healthy people
  • Presumptive: sorts likely / unlikely
  • Rapid, cheap, acceptable
  • A positive result is NOT a diagnosis

Diagnosis

  • Symptomatic or screen-positive people
  • Definitive: confirmation
  • Can be slower, costlier, invasive
  • Leads to treatment

The Natural History of Disease

Screening only works during detectable pre-clinical phase (DPCP)

  • after the disease is detectable, but before symptoms.

flowchart LR
  A[Biological<br/>onset] --> B[Detectable<br/>pre-clinical phase] --> C[Symptoms<br/>appear] --> D[Outcome]

Question

If a disease has no detectable pre-clinical phase, can we screen for it?

When is screening worthwhile?

The disease

  • Important; known natural history; a recognisable early stage

The test

  • Valid, simple, safe, acceptable, cheap

The follow-through

  • Treatment exists; facilities available;
  • agreed policy on whom to treat;
  • a continuous process, not a one-off

Comparing the test to the truth

Disease status (the gold standard) in columns

Test result in rows.

Disease + Disease −
Test + TP FP
Test − FN TN


  • TP correctly caught
  • TN correctly cleared
  • FP false alarm
  • FN missed case: often the most dangerous

Imagine a case

1,000 antenatal women, 10% prevalence

Test is 90% sensitive and 90% specific.

HIV + HIV − Total
Test + 90 90 180
Test − 10 810 820
Total 100 900 1000

Sensitivity

\[Sensitivity = \frac{TP}{(TP + FN)}\] \[= \frac{90}{(90 + 10)}\] \[= 90/100 \]

\[= 90%\]

Specificity

\[Specificity = \frac{TN}{(TN + FP)}\] \[= \frac{810}{(810 + 90)}\] \[= 810/900\] \[= 90%\]

The two mnemonics

Important

SnNOUT — a highly Sensitive test, when Negative, rules disease OUT.

Important

SpPIN — a highly Specific test, when Positive, rules disease IN.

Both are column properties — measured within the diseased or the healthy.

They are fixed by the test and do not change with prevalence.

Screening favours sensitivity (don’t miss cases);

Confirmation favours specificity (don’t falsely label).

Where you draw the line — explore

The cut-off trade-off

From the tool: move the cut-off and you trade sensitivity against specificity.

  • Cut-off low → sensitivity ↑, specificity ↓ (a screening / rule-out setting)


  • Cut-off high → specificity ↑, sensitivity ↓ (a confirmatory / rule-in setting)


You can push both up at once only by using a better test — one where diseased and healthy overlap less.

The patient’s question

  • Sensitivity asks: “If diseased, will the test catch it?”

The patient asks the question: “My test is positive — do I have the disease?”

Positive Predictive Value (PPV)

\[PPV= \frac{TP}{(TP + FP)}\] \[= \frac{90}{(90 + 90)}\] \[= 90 / 180 \] \[= 50%\]

Negative Predictive Value (NPV)

\[NPV = \frac{TN}{(TN + FN)}\] \[= \frac{810}{(810 + 10)}\] \[= 810 / 820 \] \[= 98.8%\]

Back to the 90% question

The test is 90% sensitive and 90% specific.


Yet at 10% prevalence, a positive result is correct only 50% of the time.

Important

“90% accurate” does not mean a positive result is 90% likely to be true.

Now drop the prevalence to 1%

Same test (90% / 90%), same 1,000 women — but only 10 now have HIV.

HIV + HIV − Total
Test + 9 99 108
Test − 1 891 892
Total 10 990 1000

\[PPV= \frac{TP}{(TP + FP)}\]

PPV = 9 / 108 = 8.3% — sensitivity and specificity did not move; prevalence did.

The 2×2 and 1,000 people

PPV rides on prevalence

What this means clinically

  • Screen high-prevalence / high-risk groups: PPV is far better there
  • A positive screen is a flag, not a diagnosis: always confirm
  • Mass-screening a low-prevalence population floods the system with false positives (anxiety, cost, harm)

Important

Predictive value depends on prevalence; sensitivity and specificity do not.

Confirm the positive

Series vs parallel testing

  • Positive only if both tests positive
  • Specificity ↑, PPV ↑ — strips out false positives
  • Sensitivity falls a little
  • The rule: confirm a positive screen
  • Positive if either test positive
  • Sensitivity ↑ — miss fewer cases
  • Specificity and PPV fall
  • Used when missing a case is unacceptable

Lead-time bias

Screening moves the date of diagnosis earlier.

  • Survival measured from diagnosis looks longer…
  • …even if the patient dies at the same moment

Important

You didn’t add life — you added years of knowing.

Length-time bias

Screening preferentially catches slow-growing disease.

  • Slow disease has a long detectable window → more likely to be caught by a screen
  • Fast, aggressive disease surfaces between rounds → missed
  • So screen-detected cases look to do better — an artefact

Lead-time & length-time bias

Take-home messages

  1. Screening ≠ diagnosis
  2. It needs a detectable pre-clinical phase and available treatment
  3. Sensitivity detects disease (SnNOUT) : fixed by the test
  4. Specificity detects health (SpPIN) : fixed by the test
  5. PPV / NPV answer the patient’s question and depend on prevalence
  6. Low prevalence → low PPV → always confirm a positive screen

One-slide summary


Measure Formula Depends on prevalence?
Sensitivity TP / (TP + FN) No; fixed by test
Specificity TN / (TN + FP) No; fixed by test
PPV TP / (TP + FP) Yes
NPV TN / (TN + FN) Yes

References

  • Wilson JMG, Jungner G. Principles and practice of screening for disease. WHO Public Health Papers No. 34. Geneva: WHO; 1968.
  • Gordis L. Epidemiology. 6th ed. Philadelphia: Elsevier; 2019.
  • Park K. Park’s Textbook of Preventive and Social Medicine.

Thank you