Ninety Percent Sensitive Based on How Many Cases?
October 14, 2026 · 5 min read · Aqrab editorial team
A diagnostic paper reports 90% sensitivity. Before deciding that the test rarely misses the target condition, ask a smaller question: 90% of how many people who actually had it? The denominator controls how precisely the study can estimate sensitivity.
Same Headline, Different Evidence
These are hypothetical studies, not results for a real test. Assume each participant has a suitable reference-standard result and contributes once. Sensitivity is the proportion testing positive among participants with the target condition.
| Study | Detected / condition-positive | Sensitivity | 95% interval |
|---|---|---|---|
| A | 18 / 20 | 90% | 69.9%–97.2% |
| B | 180 / 200 | 90% | 85.1%–93.4% |
Both point estimates are identical. Study A, however, remains compatible with substantially lower sensitivity under this interval method. A reader who sees only “90%” misses that distinction.
The practical takeaway
Read sensitivity as a fraction and an interval: detected / condition-positive, with a confidence interval. Do the same for specificity using the condition-negative denominator.
Why the Total Sample Size Can Mislead
A study may enroll many people but include few with the target condition. Its sensitivity estimate is informed by those condition-positive participants, not the full enrollment. Specificity uses the condition-negative group. A single overall sample-size number therefore cannot tell you whether both estimates are precise enough for the intended use.
Precision is not validity. A narrow interval will not repair an unsuitable reference standard, selective verification, unrepresentative participants, or repeated specimens treated as independent people. These hypothetical intervals illustrate sampling uncertainty only; they do not quantify those biases.
A Four-Line Appraisal
- Count the cases: How many reference-standard-positive participants contributed to sensitivity?
- Count the non-cases: How many reference-standard-negative participants contributed to specificity?
- Read the interval: Does its lower or upper end change the decision the test is meant to support?
- Check the design: Were the reference standard, missing results, participant selection, and sample-size rationale reported?
There is no universal acceptable interval width: the clinical role and consequences of missed or false-positive results determine what precision would be useful.
Where Aqrab Fits
When reviewing a diagnostic paper with Aqrab, make the numerator, denominator, interval, reference standard, and intended-use population explicit. The headline percentage is a starting point for appraisal—not a verdict on whether the test is ready to guide care.
Source Anchors
STARD 2015 asks authors to report the intended sample size and its rationale (item 18), the result cross-tabulation (item 23), and accuracy estimates with precision such as 95% confidence intervals (item 24). The FDA diagnostic-test reporting guidance recommends showing sensitivity and specificity as fractions and percentages with two-sided 95% intervals. The table above is an original arithmetic illustration, not a result from either source.
Keep reading
Don't stop at one method.
Good methods judgment comes from contrast. Read the neighboring guides, see where the assumptions diverge, and avoid treating every observational problem like it needs the same hammer.
Test Agreement Is Not Diagnostic Accuracy
A worked 97% agreement example shows why matching another imperfect test cannot establish sensitivity or specificity, plus four questions for appraising the comparator and denominators.
A Negative Test Is Not a Rule-Out: Calculate the Risk Left Behind
A worked negative likelihood-ratio example shows why the same negative test can leave very different residual risks—and what to check before calling a result reassuring.
The Trial Ended. Who Made It Into the Open-Label Extension?
A denominator-first audit of long-term extension findings: trace who enrolled, who stayed, and what an uncontrolled extension can actually establish.