Specialty › Power (hypothesis tests)

AUC

Power analysis for a single AUC against 0.5 uses the Hanley-McNeil standard error.

What is AUC?

AUC SE depends on AUC value and the ratio κ = n_neg / n_pos. Hanley-McNeil gave the closed form; we solve for the missing piece given the others. Common cut-off: AUC = 0.7 with κ = 1 (balanced) needs about 80 positives and 80 negatives for 80% power.

When should I use AUC?

  • Powering a single-marker diagnostic study.

What data does it need?

AUC + κ = n_neg / n_pos + α + n_pos or power.

What does it report?

n_pos / n_neg + achieved power + detectable AUC.

How do I interpret the result?

Imbalanced designs (κ ≫ 1, lots of negatives) buy you precision relatively cheaply on the FPR side but don't help the TPR side — for cohort studies of rare outcomes plan accordingly.

See also

References

  • Hanley & McNeil (1982). The meaning and use of the area under a ROC curve. Radiology 143(1).