Sample size for diagnostic accuracy studies

Ethics committees and reviewers increasingly reject the classic answer to the sample-size question — a screenshot of a power calculator with α=0.05, power=0.80 and an effect size of unclear origin. For diagnostic accuracy studies this answer is not just weak; it is usually the wrong kind of calculation altogether. Here is the version that survives review, with worked numbers.

Most accuracy studies are estimation, not testing

"What is the sensitivity of this test?" is not a hypothesis test. It is an estimation problem: you want to report sensitivity with a confidence interval narrow enough to be clinically meaningful. The sample size therefore comes from the interval half-width you are willing to accept, not from a power calculation^[1].

Worked example: expecting sensitivity around 0.85 and wanting a 95% confidence interval of ±0.05 requires about 196 diseased cases (Wilson interval). Aim for sensitivity 0.90 with the same precision and it drops to about 141. Two details matter here:

• Use the Wilson interval, not the Wald approximation. Near the extremes (sensitivity above 0.9, where diagnostic tests live) the Wald formula understates the required sample and produces intervals that misbehave^[1].
• Sensitivity and specificity are sized separately. Sensitivity needs diseased cases; specificity needs non-diseased. Whichever requires more screening determines the study.

A hypothesis test is the right tool only when the question genuinely is comparative: "is sensitivity above the 80% threshold that makes the test clinically useful?" — a one-sided single-proportion test — or "is test A better than test B?". Name the question before you open the calculator; a reviewer who cannot tell which question you asked will query every number that follows.

The prevalence step everyone skips

The calculation says 196 diseased cases. The feasibility question is different: how many patients must you screen to find them? With 20% disease prevalence in your recruitment stream, 196 diseased cases means roughly 980 consecutive patients screened. Divide that by your monthly eligible volume before writing "single-centre study, 12 months" — the division frequently reveals that you need a second centre.

Two rules for the prevalence number itself: take it from your own case mix, not from population studies (referral centres can run several times the population prevalence), and cite where it came from. Then inflate for losses — unreadable images, missing reference standard, withdrawals. At 10% expected loss, the 196 target becomes 218 (n / (1 − loss rate)); estimate the loss rate from your own archive's technically-inadequate-exam rate, not from hope.

Paired designs: the discordant-pair mistake

Comparing two tests in the same patients (the strongest design, and the most common in imaging) calls for McNemar's test — and the most common error in the field: sizing the study on the difference in sensitivities. The sample size is driven by the discordant pairs — cases where the tests disagree — not by the difference itself^[4]. If test A uniquely detects 15% of cases and test B uniquely detects 5%, you need about 155 diseased pairs. If the two tests agree on almost everything, even a large apparent difference requires an enormous sample.

The uncomfortable consequence: the discordance rates cannot be derived from published sensitivities. They come from a pilot, or from a prior study that applied both tests to the same patients. If you do not have them, say so and present a sensitivity table over a plausible range — committees trust an honest table more than a confident fabrication.

Verification bias: not a sample-size problem

One design flaw no sample size can fix: applying the reference standard only to patients who test positive on the index test. This inflates sensitivity and deflates specificity (verification / work-up bias), and enlarging the study makes the biased estimate more precise, not more true. Either verify all patients, or pre-specify a partial-verification correction, and state which in the protocol — STARD items 12–13 exist precisely for this^[6].

The paragraph your protocol needs

"The primary aim is estimation of sensitivity and specificity. Assuming sensitivity of 0.85 (based on [citation]), a Wilson 95% confidence interval of ±0.05 requires 196 diseased cases. With disease prevalence of 20% in our consecutive referral population (institutional data, [year]), approximately 980 patients will be screened; the target is inflated to 218 diseased cases to allow for 10% unevaluable examinations. The reference standard will be applied to all enrolled patients regardless of index test result."

Every number in that paragraph has a source a reviewer can check. That — not the software used — is what makes a sample-size section pass.

Quick reference

Sources and standards

1. Newcombe RG. Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in Medicine, 1998.
2. Cohen J. Statistical Power Analysis for the Behavioral Sciences, 1988.
3. ICH E9: Statistical Principles for Clinical Trials. ich.org
4. Connor RJ. Sample size for testing differences in proportions for the paired-sample design. Biometrics, 1987.
5. G*Power (Faul et al., 2007) and the R pwr / presize packages.
6. STARD 2015 — Standards for Reporting Diagnostic Accuracy Studies. equator-network.org

Ready-made calculators: precision-based sensitivity/specificity, sensitivity vs threshold and McNemar — free, running the same deterministic engine as this guide's numbers.