What Is Integrated Discrimination Improvement (IDI)? A Clear Guide with Example

🧪 What Is IDI?

While Net Reclassification Improvement (NRI) focuses on category shifts, IDI measures how much the new model improves average predicted probabilities for cases and non-cases across all thresholds—without relying on arbitrary cutoffs.

Key Idea:

IDI tells you how much better the new model separates diseased from non-diseased individuals.

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📐 The IDI Formula

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🧪 Conceptual Analogy

Think of a scatter plot of predicted probabilities:

• Good models spread cases (D=1) toward high predicted probabilities

• And spread non-cases (D=0) toward low predicted probabilities

So:

• IDI = "How much farther apart are the two clouds (D=1 vs D=0) in the new model compared to the old one?"
  

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🔢 An Example in Numbers

You are comparing two diagnostic models for early liver fibrosis:

• Model A: uses age, AST/ALT ratio

• Model A+B: adds a novel serum fibrosis biomarker

Suppose we calculate:

	Mean Predicted Probability (Cases, D=1)	Mean Predicted Probability (Non-Cases, D=0)
Model A	0.42	0.21
Model A+B	0.58	0.18

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💡 When to Use IDI?

Use IDI when:

• You're comparing models, not just tests

• You want to avoid arbitrary cutoff thresholds

• You need a continuous, overall measure of improvement

• You want a complement to AUC, NRI, and calibration metrics