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Buderer FormulaFree in-browser calculator

Diagnostic Sample Size Calculator.

Buderer's formula for diagnostic accuracy studies. Compute required sample size from expected sensitivity, specificity, prevalence, and desired CI width. Data never leaves your browser.

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Validated2026-04-05
CitableMethods and citation included

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Load example Diagnostic Sample Size data to see the full workflow

From pilot data or literature

From pilot data or literature

Expected in study population

Total width (e.g., 0.10 = ±5%)

Expected % lost to follow-up

When to use

  • Plan a single-arm diagnostic accuracy study (no comparison group)
  • Determine how many diseased and non-diseased subjects you need to achieve target CI width
  • Explore sample size trade-offs across different prevalence and precision scenarios
  • Justify sample size in a grant application or study protocol using Buderer's formula
  • Account for expected dropout when planning enrollment targets

Do not use for

  • Two-group hypothesis testing (comparing treatments) — use a standard power/sample size calculator
  • ROC curve comparison studies — specialized AUC comparison sample size methods are needed
  • Already collected data — use the Diagnostic Test Calculator to analyze your results

Low prevalence dramatically inflates total sample size

If you need 100 diseased subjects and prevalence is 50%, you need 200 total. At 1% prevalence, you need 10,000 total. Diagnostic studies in low-prevalence conditions are expensive because most enrolled subjects are non-diseased. Use the scenario grid to plan realistically.

Use conservative estimates when uncertain

When you do not know the expected sensitivity or specificity, use values closer to 0.50 — this produces the largest (most conservative) sample size and avoids under-powering. Better to over-enroll than to finish with an unacceptably wide CI.

Size for both sensitivity AND specificity

The tool takes the larger of the two requirements by default. If one measure matters more clinically (e.g., sensitivity for screening), you can focus on that, but always report the achieved precision for the other measure.

Standard power analysis does not apply here

Generic sample size calculators (for t-tests or chi-squared) assume two-group comparisons. Single-arm diagnostic accuracy studies use Buderer's formula, which sizes for CI width around sensitivity and specificity — a fundamentally different calculation.

1

Method

Sample size is computed using Buderer's formula: n_diseased = z2\text{z}^{2} ×\times Sens ×\times (1−Sens) / W2\text{W}^{2} for sensitivity, and n_healthy = z2\text{z}^{2} ×\times Spec ×\times (1−Spec) / W2\text{W}^{2} for specificity. Total N = max(n_diseased/prevalence, n_healthy/(1−prevalence)). An optional dropout adjustment inflates the total by 1/(1−dropout_rate). The scenario grid varies CI width and prevalence to show sample size sensitivity. All calculations run client-side in the browser.

2

Validated

Last validated 2026-04-05. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.

3

How to cite

How to Cite

ConductScience Diagnostic Sample Size Calculator (v1.0). ConductScience, Inc. 2026. Available at: https://conductscience.com/tools/diagnostic-sample-size-calculator

Buderer NMF. Statistical methodology: I. Incorporating the prevalence of disease into the sample size calculation for sensitivity and specificity. Acad Emerg Med. 1996;3(9):895-900. doi:10.1111/j.1553-2712.1996.tb03538.x

Diagnostic Study Sample Size

Standard power analysis (for comparing two groups) does not apply to single-arm diagnostic accuracy studies. Instead, Buderer's formula sizes the study to achieve a desired precision (CI width) for sensitivity and specificity.

The key formula for diseased subjects:

n_diseased = z2\text{z}^{2} ×\times Sens ×\times (1−Sens) / W2\text{W}^{2}

And for non-diseased subjects:

n_healthy = z2\text{z}^{2} ×\times Spec ×\times (1−Spec) / W2\text{W}^{2}

Total N = max(n_diseased/prevalence, n_healthy/(1−prevalence))

This ensures both sensitivity and specificity are estimated with the desired precision.

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