Mammography, by the numbers

Worth the Test · Educational analysis · Updated September 2026

A positive screening mammogram usually means further assessment is needed. It does not carry the same predictive value as a biopsy. This example shows how that distinction emerges from the denominators, and how a seemingly small choice of prevalence changes the answer.

Detection rate is not prevalence

Lehman and colleagues’ Breast Cancer Surveillance Consortium study reported 5.1 detected cancers and 0.8 false-negative cancers per 1,000 screens, with sensitivity 86.9% and specificity 88.9%. The detected cases omit the missed cases. For this illustration, adding 5.1 and 0.8 gives an approximate prevalence of 5.9 per 1,000, or 0.59%.

These are rounded study summaries, so combining them reconstructs an approximate cohort rather than the exact source data. An earlier version of this page used the detection rate, 0.51%, as prevalence. That counted the sensitivity loss twice and produced a PPV of 3.9%. The corrected approximation is 4.4%, consistent with the study’s reported screening PPV.

Work the cohort from the beginning

Start with 10,000 screens. At 0.59% prevalence, 59 people have cancer and 9,941 do not. Apply sensitivity only to the cancer group, and specificity only to the group without cancer:

• True positives: 59 × 0.869 = 51.271.
• False negatives: 59 × 0.131 = 7.729.
• False positives: 9,941 × 0.111 = 1,103.451.
• True negatives: 9,941 × 0.889 = 8,837.549.

Use the unrounded counts for the probability:

PPV = 51.271 ÷ (51.271 + 1,103.451) = 4.44%.

The denominator is everybody with a positive screen. About one in 23 positives in this approximation represents cancer. Dividing the rounded table cells gives a slightly different result because a diagram has to assign whole people; the underlying probability should not depend on that rounding.

The residual cancer probability after a negative is 7.729 ÷ (7.729 + 8,837.549) = 0.087%, about one in 1,144. That is smaller than the pre-test probability, but is not zero and does not address every cause of breast symptoms.

A comparison you can check

Hold sensitivity and specificity fixed and raise prevalence to an illustrative 2%. Per 1,000 screens, true positives rise to 17.38 and false positives are 108.78. PPV becomes 17.38 ÷ 126.16 = 13.78%. The model has changed the population, not improved the test. In practice, accuracy can also change with patient mix, reading practice, technology, and diagnostic definitions; holding it fixed isolates one mathematical effect.

Keep long-term screening benefit on its own denominator

The Cochrane review’s contested estimate of one breast-cancer death avoided per 2,000 women invited over ten years is a screening-program comparison. Its estimate of ten overdiagnosed cases per 2,000 invited uses that same denominator. Neither is a treatment effect among positive screens. Entering 2,000 into the treatment NNT box would apply prevalence and sensitivity again and incorrectly reduce the expected benefit.

For that review’s assumptions, the arithmetic is one death avoided and ten overdiagnosed cases per 2,000 invited over ten years. It cannot be combined directly with one round of the BCSC test-accuracy cohort to recreate a clinical trial. Invitation, attendance, repeat screens, treatment, follow-up duration, and the comparison group all matter. The NNT and NNS guide explains those distinctions.

Repeated false positives are a separate question

Elmore and colleagues estimated a 49.1% chance of at least one false-positive mammogram after ten screens in their historical cohort. Using 88.9% specificity in an independent-round calculation gives about 69.2%. The populations and periods differ, and repeated errors can be dependent, so the difference does not measure correlation by itself. The repeat-testing panel shows the independent-round result and the wider mathematically possible range.