Diagnostic Accuracy · AUC-CI

Sample Size for Estimation of AUC

Plan sample size for estimating one area under the ROC curve using the Hajian-Tilaki binormal approximation.

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 studies or literature

Expected AUC (%)

Enter the expected AUC based on pilot data, previous studies, or a clinically comparable population.

3. Information to be decided by the researcher

Desired margin of error (%)

This is the desired half-width of the confidence interval. For example, 5% corresponds to approximately +/-5 percentage points around the estimated AUC.

Level of confidence (%)

Anticipated dropout/non-response (%)

Allow for participants with incomplete index-test or reference-standard data.

4. Results

Enter the AUC estimation assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher evaluates a blood biomarker for early sepsis and wants to estimate its ROC area under the curve with a prespecified confidence-interval precision.

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 implements the Hajian-Tilaki binormal-approximation method for estimating one AUC with either balanced 1:1 reference-standard groups or consecutive/cross-sectional recruitment using an anticipated prevalence.

a = sqrt(2) x Z(AUC)

C = 0.0099 x exp(-a^2 / 2)

Balanced 1:1: n raw per group = Z^2 x C x (6a^2 + 16) / d^2

n analysable per group = ceiling(n raw per group)

n recruit per group = ceiling(n analysable per group / (1 - dropout))

Total analysable = 2 x n analysable per group

Total recruitment = 2 x n recruit per group

Consecutive/cross-sectional: N raw = (Z^2 x C / d^2) x [(5a^2 + 8) / prevalence + (a^2 + 8) / (1 - prevalence)]

N analysable = ceiling(N raw)

N recruitment = ceiling(N analysable / (1 - dropout))

Method references

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

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Estimation of AUC (AUC-CI).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/diagnostic-accuracy/auc-estimation/.