What Is Net Reclassification Improvement (NRI)? A Simple Guide with Examples

🧠 What Is NRI?

The Net Reclassification Improvement (NRI) is a way to measure how much better a new diagnostic model or test is at correctly classifying people compared to an old model.

It tells us whether the new model moves people into more appropriate risk categories:

Higher probability for those with the disease (D = 1)
Lower probability for those without the disease (D = 0)

📐 The Formula Explained

Breakdown of NRI Formula

$NRI = [P (up | D = 1) - P (down | D = 1)] + [P (down | D = 0) - P (up | D = 0)]$

Part 1: $P (up | D = 1)$

The proportion of true cases (D=1) who are moved up to a higher risk category in the new model.

🔼 Good! We're now more likely to treat or investigate these patients.

Part 2: $P (down | D = 1)$

The proportion of true cases who are moved down in the new model.

🔻 Bad! We're now less likely to correctly diagnose or treat them.

Part 3: $P (down | D = 0)$

The proportion of non-cases (D=0) who are moved down in the new model.

✅ Good! We're avoiding over-testing or over-treatment.

Part 4: $P (up | D = 0)$

The proportion of non-cases who are moved up.

❌ Bad! We're more likely to falsely label or overtreat them.

🔢 An Example with Numbers

Suppose we apply a new diagnostic model to 100 people:

40 have the disease (D=1)
60 do not (D=0)

In comparison to the old model, here’s what happened:

NRI Calculation Example

Among 40 Patients with Disease (D=1):

🔼 12 moved up (good): $P (up | D = 1) = \frac{12}{40} = 0.30$
🔻 4 moved down (bad): $P (down | D = 1) = \frac{4}{40} = 0.10$

Among 60 Patients without Disease (D=0):

✅ 15 moved down (good): $P (down | D = 0) = \frac{15}{60} = 0.25$
❌ 9 moved up (bad): $P (up | D = 0) = \frac{9}{60} = 0.15$

Plug into NRI formula:

NRI = (0.30 - 0.10) + (0.25 - 0.15) = 0.20 + 0.10 = 0.30

🎯 Interpretation:

The new model improved net classification by 30% overall.
That means it correctly moved more people into the “right direction” than the wrong one.

🔍 Summary Table

Direction of Movement	Group	Effect on Accuracy	Good or Bad?
Upward	D = 1	More likely to detect	✅ Good
Downward	D = 1	Misses diagnosis	❌ Bad
Downward	D = 0	Avoids overtreatment	✅ Good
Upward	D = 0	Increases false positives	❌ Bad