Diagnostic Accuracy · AUC-1S

Sample Size for Testing One AUC

Plan sample size for testing whether a diagnostic test's anticipated ROC AUC is better than a prespecified benchmark.

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

Benchmark / minimum acceptable AUC under the null hypothesis (%) AUC0

The fixed AUC under the null hypothesis. It may represent the performance of an existing test, a published benchmark, or the minimum clinically acceptable level of discrimination.

3. Information decided by the researcher

Target clinically important improvement (%) Delta = AUC1 - AUC0

The smallest improvement above the benchmark AUC that the study should be powered to detect.

Anticipated AUC under the alternative hypothesis (AUC1): 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.

4. Results

Enter the one-AUC testing assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher tests whether a new cardiac biomarker discriminates patients with and without acute myocardial infarction better than a prespecified benchmark AUC.

Formula and methodological note

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 = AUC0 against H1: AUC = AUC0 + Delta, where AUC1 is greater than AUC0. It uses Hajian-Tilaki's binormal approximation with the standard-deviation ratio assumed approximately 1.

H0: AUC = AUC0

H1: AUC = AUC0 + Delta = AUC1

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

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

n per group = ceiling([Z alpha x sqrt(V(AUC0)) + Z power x sqrt(V(AUC1))]^2 / Delta^2)

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

N = ceiling([Z alpha x sqrt(W(AUC0, prevalence)) + Z power x sqrt(W(AUC1, 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 a single diagnostic test with a continuous or ordinal index test and a binary reference standard. It does not cover paired AUC comparison, clustering, repeated lesions within participants, or multiple-reader ROC studies.

Method references

Hajian-Tilaki K. Sample size estimation in diagnostic test studies of biomedical informatics. Journal of Biomedical Informatics. 2014;48:193-204. Eq. 7.5; variance from Eq. 7.4 / Appendix B.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Testing One AUC (AUC-1S).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/diagnostic-accuracy/one-auc/.