A screening test for gestational diabetes has a sensitivity of 80% and a specificity of 85%. Among 1000 pregnant women screened, 50 actually have gestational diabetes. How many women will receive a false positive result?

Explanation

## Calculating False Positives from Sensitivity and Specificity **Key Point:** False positives occur in the disease-free population. The number of false positives depends on specificity and the total number of disease-free individuals, NOT on sensitivity. ### Step-by-Step Calculation Given: - Total population = 1000 women - Disease-positive (truly have GDM) = 50 - Disease-negative (truly do not have GDM) = 1000 − 50 = 950 - Sensitivity = 80% - Specificity = 85% ### Formula for False Positives $$\text{False Positives} = (1 - \text{Specificity}) \times \text{Number of Disease-Free}$$ $$\text{False Positives} = (1 - 0.85) \times 950$$ $$\text{False Positives} = 0.15 \times 950 = 142.5 \approx 142$$ ### Verification with 2×2 Contingency Table | | **Disease Present** | **Disease Absent** | **Total** | |---|---|---|---| | **Test Positive** | TP = 0.80 × 50 = 40 | FP = 0.15 × 950 = 142.5 | 182.5 | | **Test Negative** | FN = 0.20 × 50 = 10 | TN = 0.85 × 950 = 807.5 | 817.5 | | **Total** | 50 | 950 | 1000 | **High-Yield:** False positives = (1 − Specificity) × Disease-free population. In this case, 0.15 × 950 = 142.5 ≈ **142** women will test positive despite not having GDM. Option B (Approximately 142) is therefore correct. ### Why Other Options Are Wrong - **Option A (~95):** Does not correspond to any standard calculation using the given values. - **Option C (~10):** This equals the number of **false negatives** (FN = 0.20 × 50 = 10), not false positives — a common confusion. - **Option D (~127):** Does not correspond to any standard calculation; likely a distractor. ### Clinical Implications for GDM Screening **Clinical Pearl:** In gestational diabetes screening, a high false positive rate (14.7% of disease-free women) is often acceptable because: 1. The condition carries significant maternal and fetal morbidity if missed 2. Confirmatory testing (oral glucose tolerance test) is readily available 3. False positives lead to further evaluation, not immediate treatment **Warning:** Do not confuse false positives with the false positive rate. False positive rate = (1 − Specificity), whereas the **number** of false positives also depends on how many disease-free individuals are in the population. (Park's Textbook of Preventive and Social Medicine; KD Tripathi Essentials of Medical Pharmacology — biostatistics principles)