Sensitivity Calculation for the New Breast Cancer Screening Test
The sensitivity of the new screening test is 90%.
Calculation Method
To calculate sensitivity, you need to determine what proportion of all true disease cases the test correctly identifies. The formula is:
Sensitivity = True Positives / (True Positives + False Negatives)
Step-by-Step Analysis
From the question data:
- The reference test detected 180 cases with 20 false negatives
- This means the reference test had: 180 true positives + 20 false negatives = 200 total actual disease cases
- The new test detected 200 positive cases in the same 1000 patients
Since there are 200 total actual disease cases (established by the reference standard), and the new test detected 200 positive cases:
- True Positives = 180 (the cases both tests detected)
- False Negatives = 20 (the cases the new test missed)
Sensitivity = 180 / (180 + 20) = 180 / 200 = 0.90 = 90%
Context from Screening Literature
This 90% sensitivity falls within the expected range for breast cancer screening modalities. Mammography screening demonstrates sensitivity of 77% to 95% across different populations and technical factors 1. The U.S. Preventive Services Task Force reports that screening mammography has sensitivity of approximately 77% to 95% and specificity of about 94% to 97% 1.
The answer is 90%.