PPV and NPV 

Dr. Arvind Kumar

1. PPV and NPV 

PPV (Positive Predictive Value)

  • Definition: If a test is positive, PPV tells you how likely it is that the person really has the disease.

  • Formula:
    PPV = TP / (TP + FP)
    (Out of all who tested positive, how many are truly positive?)

Example

If 100 people test positive, but only 80 actually have the disease →
PPV = 80 / 100 = 80%

NPV (Negative Predictive Value)

  • Definition: If a test is negative, NPV tells you how likely it is that the person really does NOT have the disease.

  • Formula:
    NPV = TN / (TN + FN)
    (Out of all who tested negative, how many are truly negative?)

Example

If 200 test negative and 190 truly do not have the disease →
NPV = 190 / 200 = 95%

2. How Prevalence Affects PPV & NPV (Very Important Concept)

Think of prevalence = how common the disease is in the population.

When prevalence is high

  • More people actually have the disease
    → PPV increases (positive test more believable)

  • NPV decreases (a negative test becomes less trustworthy)

When prevalence is low

  • PPV decreases (many positive tests may be false positives)

  • NPV increases (negative test is very reliable)

Simple Example

Imagine a rare disease (1% prevalence):

  • Even with a good test, many positives will be false → PPV low

  • Most people don’t have disease → NPV high

👉 Key sentence:
Sensitivity & specificity are properties of the test;
PPV & NPV are properties of the test in a population.

3. ROC Curve & AUC (Simple Explanation)

ROC Curve (Receiver Operating Characteristic curve)

  • A graph that shows how a test performs at different cutoffs.

  • X-axis: 1 – Specificity (False Positive Rate)

  • Y-axis: Sensitivity (True Positive Rate)

You change cutoff → sensitivity and specificity change → ROC points.

AUC (Area Under the Curve)

  • AUC tells you how good the test is overall.

  • AUC = 1.0 → perfect test

  • AUC = 0.5 → useless test (same as coin toss)

  • AUC = 0.7–0.8 → acceptable

  • 0.8–0.9 → good

  • >0.9 → excellent

👉 Simple meaning:
AUC tells the probability that the test will correctly rank a sick person higher than a healthy person.

4. Calculate Sensitivity & Specificity From Real Data

You must have a 2×2 table:

Disease + Disease –
Test Positive TP FP
Test Negative FN TN

Formulas

  • Sensitivity = TP / (TP + FN)
    “Out of all diseased, how many were detected?”

  • Specificity = TN / (TN + FP)
    “Out of all healthy, how many were correctly identified?”

✅ Example (Real Data Example)

Suppose:

  • TP = 65

  • FN = 35

  • TN = 120

  • FP = 30

Sensitivity

= 65 / (65 + 35)
= 65 / 100
= 65%

Specificity

= 120 / (120 + 30)
= 120 / 150
= 80%

PPV

= 65 / (65 + 30)
= 65 / 95 = 68.4%

NPV

= 120 / (120 + 35)
= 120 / 155 = 77.4%

5. Interpreting Biomarker Cutoffs 

Every biomarker (BNP, CRP, troponin, etc.) has a “cutoff value.”

What does cutoff mean?

A number above (or below) which the test is considered positive.

Selecting a cutoff

  • Low cutoff → high sensitivity, low specificity
    Good for screening (don’t miss cases)

  • High cutoff → high specificity, low sensitivity
    Good for confirmation (avoid false positives)

Optimal cutoff

Usually chosen using:

  • Youden Index (Sensitivity + Specificity – 1)

  • Best point on ROC curve (closest to top-left corner)