Key Facts

Sensitivity and specificity are fundamental to understanding diagnostic test performance. They are intrinsic properties of a test (fixed regardless of prevalence), while predictive values vary with disease prevalence in the tested population.

2×2 Table

Formulae

• Sensitivity = a / (a + c)
• Specificity = d / (b + d)
• PPV = a / (a + b)
• NPV = d / (c + d)
• Prevalence = (a + c) / (a + b + c + d)
• Accuracy = (a + d) / (a + b + c + d)

Clinical Mnemonics

• SnNOUT: if a test has high Sensitivity, a Negative result rules OUT disease
• SpPIN: if a test has high Specificity, a Positive result rules IN disease

Trade-off Between Sensitivity and Specificity

• Adjusting the test cut-off point affects both: increasing sensitivity decreases specificity and vice versa
• The optimal cut-off depends on the clinical context (consequences of false positives vs false negatives)
• Screening tests prioritise high sensitivity (don't miss disease)
• Confirmatory tests prioritise high specificity (don't falsely diagnose)

Clinical Examples

• D-dimer for PE: highly sensitive (~95%) but poorly specific (~40%); negative D-dimer rules out PE (SnNOUT)
• Troponin for MI: highly sensitive and specific with hs-troponin assays
• Anti-CCP for RA: highly specific (~96%) but less sensitive (~67%); positive result strongly supports RA (SpPIN)
• RADT for GAS pharyngitis: high specificity (~95%) but moderate sensitivity (~70-90%)

Effect of Prevalence on Predictive Values

• In high-prevalence settings: PPV increases, NPV may decrease
• In low-prevalence settings: PPV decreases (more false positives), NPV increases
• This is why screening in low-prevalence populations produces many false positives
• Pre-test probability (clinical suspicion + prevalence) is essential for interpreting test results

ROC Curve Analysis

• Receiver Operating Characteristic curve
• Plots sensitivity (true positive rate) on y-axis against 1−specificity (false positive rate) on x-axis
• Each point on the curve represents a different cut-off value
• AUC (area under the curve) summarises overall test performance
• AUC interpretation: 1.0 = perfect, 0.5 = no discriminatory value (diagonal line)
• Optimal cut-off: point nearest top-left corner (maximises both sensitivity and specificity)

Likelihood Ratios

• Convert pre-test probability to post-test probability
• LR+ >10: large and often conclusive increase in probability
• LR+ 5-10: moderate increase
• LR+ 2-5: small increase
• LR− <0.1: large and often conclusive decrease in probability
• LR− 0.1-0.2: moderate decrease
• LR− 0.2-0.5: small decrease
• Can be used with Fagan nomogram for bedside estimation

Choosing the Right Test

• Screening: choose high sensitivity (minimise false negatives; don't miss disease)
• Confirmation: choose high specificity (minimise false positives; don't falsely diagnose)
• Sequential testing: screen with sensitive test → confirm with specific test

Clinical Application

• Always consider pre-test probability before ordering tests
• A test is most useful when pre-test probability is intermediate (50%)
• Tests add little information when pre-test probability is very high or very low
• Order of testing: history (pre-test probability) → sensitive screening test → specific confirmatory test
• Bayesian reasoning: update probability with each piece of information

• Understanding sensitivity and specificity is fundamental to evidence-based test interpretation
• Predictive values change dramatically with disease prevalence
• In rare diseases, even highly specific tests produce many false positives in population screening
• Point-of-care testing with known sensitivity/specificity allows bedside probability estimation
• AI-assisted diagnostics increasingly assessed using ROC analysis and AUC metrics

Effect of Prevalence on PPV (Example)

LR Interpretation Guide