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Calculator · deterministic

Sensitivity / specificity sample size calculator

Estimating a diagnostic test's accuracy with a confidence interval: diseased cases from the expected value and CI half-width.

Calculator

No AI, no sign-up — the arithmetic runs in the server-side deterministic solver, validated against G*Power and R pwr.

Enter 0–1: 0.85 for 85%. Take it from studies with a similar population.
The widest interval that stays clinically meaningful: ±0.05 is tight, ±0.10 loose.

When to use it

"What is this test's sensitivity?" is not a hypothesis test — it is an estimation problem: the sample size comes from the CI width you can accept, not from a power calculation. Most diagnostic accuracy studies are in this class. The full treatment is in the diagnostic accuracy guide.

Where the inputs come from

  • Expected value: from a study with a similar population; near the extremes (0.90+) the sample shrinks fast, and the Wilson method handles that correctly.
  • Do not skip the prevalence step: the result is the number of DISEASED cases; the total to screen comes from dividing by prevalence. Specificity needs the same calculation on the healthy side.

Worked example

For an expected sensitivity of 0.85 and a target 95% CI of ±0.05, the solver requires 196 diseased cases (Wilson method). If prevalence in your stream is 20%, roughly 980 consecutive patients must be screened; with 10% unevaluable exams the target rises to 218 cases.

How to write it in the protocol

Fill-in methods sentence

“The primary aim is estimation of sensitivity and specificity. For an expected sensitivity of [value] [with source], a Wilson 95% CI of ±[half-width] required [n] diseased cases; with [x]% prevalence, approximately [N] patients will be screened. The reference standard will be applied to all patients regardless of the index test result.”

Sources

  1. Cohen J. Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Lawrence Erlbaum; 1988.
  2. Faul F, Erdfelder E, Lang A-G, Buchner A. G*Power 3: a flexible statistical power analysis program. Behav Res Methods. 2007;39:175–191.
  3. Champely S. pwr: Basic Functions for Power Analysis (R package).
  4. Newcombe RG. Two-sided confidence intervals for the single proportion: comparison of seven methods. Stat Med. 1998;17:857–872.

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