A new screening test for the breast cancer is approved. Calculate sensitivity and specificity, based on the findings given below.
**Question:** A new screening test for the breast cancer is approved. Calculate sensitivity and specificity, based on the findings given below.
A. The test correctly identified 90% of breast cancer patients as positive (true positive rate)
B. The test correctly identified 95% of healthy individuals as negative (true negative rate)
C. The prevalence of breast cancer in the screened population is 5%
D. The prevalence of breast cancer in the screened population is 10%
**Correct Answer:** .
**Core Concept:**
The sensitivity (Se) and specificity (Sp) of a diagnostic test are two important parameters that help assess its performance. Sensitivity represents the ability of the test to correctly identify patients with the disease (in this case, breast cancer), while specificity indicates the ability to correctly identify individuals without the disease. Prevalence is the number of cases of the disease in the screened population.
**Why the Correct Answer is Right:**
The sensitivity (Se) is calculated as the ratio of true positive rate (TPR) to (TPR + false negative rate (FNR)). In this scenario, the sensitivity can be calculated as:
Se = TPR / (TPR + FNR) = (90% / (90% + FNR))
The specificity (Sp) is calculated as the ratio of true negative rate (TNR) to (TNR + false positive rate (FPR)). In this scenario, the specificity can be calculated as:
Sp = TNR / (TNR + FPR) = (95% / (95% + FPR))
**Why Each Wrong Option is Incorrect:**
A. False positive rate (FPR) is the percentage of healthy individuals who test positive for the disease when they do not have the disease (95% in option B). However, this option is incorrect because the formula for specificity does not involve FPR.
B. False negative rate (FNR) is the percentage of individuals with the disease who test negative for the disease (10% in option A). However, this option is incorrect because the formula for sensitivity does not involve FNR.
C. Prevalence (P) is the number of cases of the disease in the screened population (5% in option C). This option is incorrect as it does not involve calculating the test's performance.
D. False positive rate (FPR) is the percentage of healthy individuals who test positive for the disease when they do not have the disease (95% in option B). Although this option involves FPR, it is incorrect because it is used in calculating specificity, not sensitivity.
**Sensitivity:**
Sensitivity (Se) is the probability of correctly detecting true positives (individuals with breast cancer) out of all individuals with breast cancer (TPR = true positive rate) in the population. In this case, sensitivity can be calculated as:
Se = TPR / (TPR + FNR) = (90% / (90% + FNR))
**Specificity:**
Specificity (Sp) is the probability of correctly detecting true negatives (individuals without breast cancer) out of all individuals without