## Sensitivity and False Negative Rate **Key Point:** Sensitivity and the false negative rate (FNR) are complementary: they sum to 100%. If sensitivity is 85%, the false negative rate is necessarily 15%. ### Mathematical Relationship Sensitivity + False Negative Rate = 100% $$\text{Sensitivity} = \frac{TP}{TP+FN}$$ $$\text{False Negative Rate} = \frac{FN}{TP+FN} = 1 - \text{Sensitivity}$$ Therefore: FNR = 100% − 85% = **15%** ### Clinical Meaning In the cervical cancer screening context: - Sensitivity of 85% means the test correctly identifies 85% of women who actually have cervical cancer - False negative rate of 15% means 15% of women with cervical cancer will incorrectly test negative - These 15% represent women with disease who are falsely reassured — a critical safety issue **High-Yield:** A highly sensitive test is preferred for screening serious diseases (like cancer, TB, HIV) because it minimizes the risk of missing cases. The cost is a higher false positive rate, which requires confirmatory testing. ### Inverse Relationship | Sensitivity | False Negative Rate | |---|---| | 90% | 10% | | 85% | 15% | | 80% | 20% | | 70% | 30% | **Clinical Pearl:** In screening programs, sensitivity is prioritized over specificity to avoid missing cases of serious disease, even if it means more false alarms requiring follow-up.
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