Saved Search

Diagnostic Accuracy · AUC-2P

Sample Size for Comparing Two Paired AUCs

Plan sample size for comparing ROC AUCs when the same participants undergo two diagnostic tests.

1. Planning setup

Planned sampling approach

2. Information obtained from previous study/literature

Expected ROC AUC for the comparator test based on pilot data, previous studies, or a clinically comparable population.

3. Information decided by the researcher

The smallest AUC improvement for Test B above Test A that the study should be powered to detect.

Anticipated AUC of Test B: 80%

This is the anticipated correlation between the estimated AUCs because both tests are measured in the same participants. It is not the correlation between raw test values. Use pilot or previous paired-test data where available.

The significance level is calculated as alpha = 1 - confidence level.

Apply this at participant level only; do not double for Test A and Test B.

4. Results

Enter the paired-AUC comparison assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

Every patient with suspected coronary disease undergoes two imaging tests, allowing their paired ROC AUCs to be compared against the same reference diagnosis.

Formula and methodological note

Design selection: Use this calculator only when both index tests are performed in the same participants. For separate participant samples, use the independent-AUC calculator.

Scope and limitations: Use this calculator only for the diagnostic design named on this page and its stated independent or paired sampling assumptions. It does not cover clustering, repeated lesions, multiple-reader designs, prediction-model development, or non-inferiority/equivalence unless explicitly stated. The implemented normal or binormal approximation may be unsuitable near parameter boundaries or with sparse reference-standard groups. Where prevalence is used, it supports recruitment planning and does not necessarily form part of the core precision or hypothesis-test calculation.

This calculator tests H0: AUC_A = AUC_B against H1: AUC_B = AUC_A + Delta for paired diagnostic tests performed in the same participants.

AUC_H0 = (AUC_A + AUC_B) / 2

a(x) = sqrt(2) x Phi^-1(x)

Balanced 1:1: V(x) = 0.0099 x exp[-a(x)^2 / 2] x [6a(x)^2 + 16]

D0 = 2 x V(AUC_H0) x (1 - rho)

D1 = V(AUC_A) + V(AUC_B) - 2 x rho x sqrt[V(AUC_A) x V(AUC_B)]

n = ceiling([Z alpha x sqrt(D0) + Z power x sqrt(D1)]^2 / Delta^2)

Consecutive/cross-sectional uses W(x, prevalence) = 0.0099 x exp[-a(x)^2 / 2] x [(5a(x)^2 + 8) / prevalence + (a(x)^2 + 8) / (1 - prevalence)]

D0_cross = 2 x W(AUC_H0, prevalence) x (1 - rho)

D1_cross = W(AUC_A, prevalence) + W(AUC_B, prevalence) - 2 x rho x sqrt[W(AUC_A, prevalence) x W(AUC_B, prevalence)]

N = ceiling([Z alpha x sqrt(D0_cross) + Z power x sqrt(D1_cross)]^2 / Delta^2)

Methodological note: This calculator is intended for superiority testing of two ROC AUCs from paired diagnostic tests performed in the same participants, with continuous or ordinal index-test results and a binary reference standard. It does not cover independent samples, non-inferiority or equivalence designs, clustering, repeated lesions, multiple readers, partial AUCs, or prediction models developed and evaluated in the same dataset.

Method references

  1. Hajian-Tilaki K. Sample size estimation in diagnostic test studies of biomedical informatics. Journal of Biomedical Informatics. 2014;48:193-204. Eq. 7.6-7.9; Table 8.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Comparing Two Paired AUCs (AUC-2P).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/diagnostic-accuracy/two-paired-aucs/.