Diagnostic Test Evaluation

The Clinician’s Toolkit for Measuring How Well Tests Work

Learning Objectives

  1. Construct a 2×2 table with index test in rows, gold standard in columns
  2. Calculate sensitivity, specificity, PPV, NPV from the 2×2 table
  3. Explain how prevalence transforms predictive values
  4. Compute and interpret likelihood ratios (LR+, LR−)
  5. Use the Fagan nomogram for pre-test → post-test probability
  6. Construct and interpret ROC curves and AUC
  7. Choose wisely: when to prioritise sensitivity vs specificity

Clinical Hook: Cervical Cancer Screening in Rural India

India bears ¼ of the global cervical cancer burden.

Rural districts lack Pap smear infrastructure — so the government promotes VIA (Visual Inspection with Acetic Acid).

A community health worker screens 1000 women with VIA. Results are compared against colposcopy-directed biopsy.

Test Sensitivity Specificity
VIA 80% 85%
Pap Smear 60% 95%

“VIA is more sensitive — isn’t it the better test?”

It depends on what you need the test to do.

The 2×2 Contingency Table

Standard layout: Index test in rows, gold standard in columns.

Convention Alert

FP is in the top-right corner (test +, disease −). Most textbooks, NEET PG, and USMLE follow this layout.

VIA Screening: 1000 Women Icon Array

Sensitivity and Specificity

Sensitivity (True Positive Rate)

\[\text{Sens} = \frac{TP}{TP + FN}\]

“Of patients WITH disease, how many test positive?”

. . .

VIA: \(\frac{40}{50} = 80\%\)

Pap: \(\frac{30}{50} = 60\%\)

. . .

Use: Screening — don’t miss cases

Mnemonic: SnNOut — Sensitive test, Negative result, rules Out

Specificity (True Negative Rate)

\[\text{Spec} = \frac{TN}{FP + TN}\]

“Of patients WITHOUT disease, how many test negative?”

. . .

VIA: \(\frac{808}{950} = 85\%\)

Pap: \(\frac{902}{950} = 95\%\)

. . .

Use: Confirmation — don’t overdiagnose

Mnemonic: SpPIn — Specific test, Positive result, rules In

VIA vs Pap: The Sensitivity-Specificity Trade-Off

Predictive Values: What Clinicians Actually Need

Positive Predictive Value

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

“If test positive, what’s the chance of disease?”

. . .

VIA PPV = \(\frac{40}{40 + 142}\) = 22%

Pap PPV = \(\frac{30}{30 + 48}\) = 38%

At 5% prevalence, 78% of VIA positives are false alarms!

Negative Predictive Value

\[NPV = \frac{TN}{FN + TN}\]

“If test negative, what’s the chance of no disease?”

. . .

VIA NPV = \(\frac{808}{10 + 808}\) = 98.8%

Pap NPV = \(\frac{902}{20 + 902}\) = 97.8%

Both excellent for ruling out.

The Key Insight

Sensitivity and specificity are test properties. PPV and NPV depend on prevalence — the same test behaves differently in different populations!

The Prevalence Effect: VIA vs Pap

Likelihood Ratios: Prevalence-Independent

\[LR^+ = \frac{\text{Sensitivity}}{1 - \text{Specificity}}\]

\[LR^- = \frac{1 - \text{Sensitivity}}{\text{Specificity}}\]

Test LR+ LR−
VIA 5.3 0.24
Pap 12.0 0.42
LR+ Value Interpretation
> 10 Strong rule-in
5 – 10 Moderate rule-in
2 – 5 Weak evidence
LR− Value Interpretation
< 0.1 Strong rule-out
0.1 – 0.2 Moderate rule-out
0.2 – 0.5 Weak evidence

Key insight: Pap+ is more convincing (LR+ = 12 → strong rule-in), but VIA− is more reassuring (LR− = 0.24 < 0.42).

This quantifies SnNOut / SpPIn precisely.

Fagan Nomogram: VIA vs Pap

ROC Curves: Fasting Glucose for Diabetes

AUC: Summarising Test Discrimination

AUC Range Discrimination Clinical Analogy
0.90 – 1.00 Excellent Troponin for MI
0.80 – 0.90 Good GeneXpert for TB
0.70 – 0.80 Fair CRP for infection
0.60 – 0.70 Poor ESR for inflammation
0.50 None Coin flip

Practical Meaning

AUC = 0.87 means: pick one random diabetic and one random non-diabetic — there’s an 87% chance the diabetic has a higher fasting glucose.

Comparing Tests: HbA1c vs Random Blood Glucose

Test Selection: Sensitivity vs Specificity

Clinical Scenario Priority Reason Indian Example
Community screening HIGH Sensitivity Don’t miss cases VIA for cervical cancer
Confirming diagnosis HIGH Specificity Don’t overdiagnose Biopsy after VIA+
Ruling out danger HIGH Sensitivity FN = patient sent home D-dimer for PE
Low prevalence HIGH Specificity Reduce false positives HIV screening
Toxic treatment HIGH Specificity FP → unnecessary harm Chemo based on biopsy

SnNOut / SpPIn: Sensitive Negative rules Out. Specific Positive rules In.

The Two-Step Strategy: Screen Then Confirm

Indian Scenario: TB GeneXpert

Setting: Rural PHC in Bihar, TB prevalence 3%

Test: GeneXpert MTB/RIF — Sens 98%, Spec 99%

Why GeneXpert works at low prevalence:

  • LR+ = 98 — dramatically shifts probability toward TB
  • PPV = 75% — useful even at 3% prevalence
  • NPV = 99.9% — negative GeneXpert powerfully excludes TB
  • LR− = 0.02 — near-perfect rule-out

. . .

The Specificity Secret

99% specificity means only 10 false positives per 1000 non-diseased patients. Compare to 90% specificity → 100 FPs. High specificity protects PPV at low prevalence.

Indian Scenario: Malaria RDT Across Seasons

Indian Scenario: VIA “See and Treat” Model

The programme logic: In rural India where follow-up is unreliable, VIA + same-day cryotherapy catches 80% of precancers in a single visit. Test selection depends on healthcare context, not just statistics.

Key Takeaways

  1. 2×2 table — index test in rows, gold standard in columns, FP in top-right

  2. Sensitivity & specificity are test properties; PPV & NPV depend on prevalence

  3. Low prevalence destroys PPV — even good tests produce mostly false positives

  4. Likelihood ratios are prevalence-independent: LR+ > 10 = strong rule-in, LR− < 0.1 = strong rule-out

  5. ROC curves show the full sensitivity-specificity trade-off; AUC summarises discrimination

  6. Two-step strategy — screen (high sensitivity) then confirm (high specificity)

  7. Context matters — VIA was chosen for India not for best PPV, but for the “see and treat” model

Further Learning

Videos:

Textbooks:

  • Sackett DL et al. Clinical Epidemiology. 3rd ed. Ch 4 (Diagnosis).
  • Kirkwood BR. Essential Medical Statistics. 2nd ed. Ch 36.