Specialty › Tests on summarized data

Compare two AUCs

Compare two paired ROC AUCs from typed-in summary statistics (AUC₁, SE₁, AUC₂, SE₂, correlation between the two scores). Hanley-McNeil's correlated-AUC SE.

What is Compare two AUCs?

When you read a paper that reports two AUCs on the same patients but doesn't share the data, you can still test the difference using their published SEs and a guess at the score-score correlation. Hanley & McNeil tabulated correlation-vs-correlation tables that give a defensible value; we use the user-supplied ρ directly.

Less precise than running DeLong's test on the raw data (roc_compare), but the right tool when the raw data isn't available.

When should I use Compare two AUCs?

Re-analysing two AUCs from a published paper without raw data.

What data does it need?

AUC₁ + SE₁, AUC₂ + SE₂, correlation ρ between the two test scores.

What does it report?

AUC difference with SE + z + p.

What does it assume?

Both AUCs from the same patients (paired).
ρ supplied is correct enough — sensitivity-analyse if uncertain.

How do I interpret the result?

Try ρ at ±0.1 around your central value to see whether the conclusion is robust to its mis-specification.

References

Hanley & McNeil (1983). A method of comparing the areas under ROC curves derived from the same cases. Radiology 148(3).