Sensitivity Calculation for Breast Cancer Detection Device
The sensitivity of this device is 100% (Option C-90% is the closest available answer, though the actual calculated sensitivity exceeds this).
Understanding the Scenario
To calculate sensitivity, we need to identify:
- True Positives (TP): Cases correctly identified as having disease
- False Negatives (FN): Cases with disease that the device missed
- Sensitivity Formula: TP / (TP + FN)
Breaking Down the Data
From the scenario:
- Total patients tested: 1,000
- Actual breast cancer cases (confirmed by mammogram as gold standard): 800
- Device detected: All 800 mammogram-confirmed cases PLUS 50 additional cases
The key insight is that the device identified all 800 confirmed cancer cases. The 50 additional cases represent false positives (patients flagged as positive who don't actually have cancer based on mammogram), not false negatives.
Calculation
- True Positives: 800 (all confirmed cancer cases were detected)
- False Negatives: 0 (no cancer cases were missed)
- Sensitivity: 800 / (800 + 0) = 800/800 = 100%
Clinical Context
This calculated sensitivity of 100% would be exceptional and exceeds typical mammography performance. For reference, screening mammography typically demonstrates sensitivity of approximately 77-95% across all age groups 1. Even advanced modalities like MRI in high-risk populations show sensitivity ranging from 75-100% 1.
Important caveat: The 50 false positive cases would impact the device's specificity and positive predictive value, not its sensitivity. These false positives represent the 50 patients without cancer (from the 200 cancer-free patients) who were incorrectly flagged as positive, resulting in unnecessary follow-up testing and patient anxiety—a well-documented harm of breast cancer screening 1.
Given the available answer choices and that 100% exceeds option C (90%), option C-90% is the closest available answer, though the actual calculated value is higher.