Calculating Sensitivity of the New Screening Test
The sensitivity of the new screening test is 90% (180/200).
Understanding the Calculation
Sensitivity is defined as the proportion of individuals with disease (as determined by the reference standard) who test positive on the screening test. The formula is:
Sensitivity = True Positives / (True Positives + False Negatives)
Breaking Down the Numbers
In this scenario:
- Reference standard (mammogram) identified 200 women with breast cancer
- New test correctly identified 180 of these 200 women (true positives)
- New test missed 20 of these 200 women (false negatives)
- The 50 false positives among the 800 mammogram-negative women are irrelevant for sensitivity calculation
The Calculation
- True Positives = 180
- False Negatives = 20
- Total with disease (by reference standard) = 200
Sensitivity = 180/200 = 0.90 or 90%
Clinical Context
This 90% sensitivity is notably higher than the typical sensitivity range for screening mammography itself, which according to the U.S. Preventive Services Task Force is approximately 77% to 95% across all ages 1. The sensitivity of mammography varies with multiple factors including age, breast density, and time since last examination 1.
Important Caveat
This calculation assumes mammography is a perfect reference standard, which it is not. In reality, mammography has imperfect sensitivity (77-95%) and specificity (94-97%) 1. Therefore, this 90% sensitivity estimate represents the new test's performance relative to mammography, not necessarily its true sensitivity for detecting breast cancer. Some of the 20 "missed" cases might actually be false positives on mammography, and some true cancers might have been missed by both tests 1.