Diagnostic Accuracy · AUC-2I

Sample Size for Comparing Two Independent AUCs

Plan sample size for comparing ROC AUCs of two diagnostic tests evaluated in separate, independent participant samples.

1. Planning setup

Planned sampling approach

Balanced reference-standard groupsRecruit equal numbers of reference-standard-positive and reference-standard-negative participants (1:1).Consecutive / cross-sectional samplingRecruit from the target population; anticipated prevalence is required.

2. Information obtained from previous study/literature

Expected AUC of Test A / comparator test (%) AUC_A

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

3. Information decided by the researcher

Target clinically important AUC difference (%) Delta = AUC_B - AUC_A

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

Anticipated AUC of Test B: 80%

Confidence level (%)

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

Statistical power (%)

Test direction

Anticipated dropout/non-response (%)

Allow for incomplete index-test or reference-standard data in each independent test arm.

4. Results

Enter the independent-AUC comparison assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

Two imaging-based diagnostic models are evaluated in separate patient cohorts, and the researcher wants to compare their independent ROC AUCs.

Formula and methodological note

Design selection: Do not use this calculator when both tests are applied to the same participants. Use the paired-AUC calculator instead.

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 two independent diagnostic-test samples. It uses Hajian-Tilaki's binormal AUC variance approximation with the standard-deviation ratio assumed approximately 1.

H0: AUC_A = AUC_B

H1: AUC_B = AUC_A + Delta

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]

n = ceiling([Z alpha x sqrt(2 x V(AUC_H0)) + Z power x sqrt(V(AUC_A) + V(AUC_B))]^2 / Delta^2)

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

N = ceiling([Z alpha x sqrt(2 x W(AUC_H0, prevalence)) + Z power x sqrt(W(AUC_A, prevalence) + W(AUC_B, prevalence))]^2 / Delta^2)

Z alpha = Phi^-1(1 - alpha / 2) for a two-sided test, or Phi^-1(1 - alpha) for one-sided superiority.

Z power = Phi^-1(power)

Methodological note: This calculator is intended for comparison of two diagnostic tests evaluated in independent participant samples, with continuous or ordinal index-test results and a binary reference standard. It does not cover paired tests, clustering, repeated lesions, multiple readers, non-inferiority, or equivalence designs.

Method references

Hajian-Tilaki K. Sample size estimation in diagnostic test studies of biomedical informatics. Journal of Biomedical Informatics. 2014;48:193-204. Eq. 7.8; Table 7.

Suggested citation

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