Population is 10,000. Of these 20% is having disease. The screening test has 95% sensitivity and 80% specificity. PPV is-
**Core Concept**
Population screening tests are used to detect diseases in asymptomatic individuals. In this context, sensitivity refers to the test's ability to correctly identify those with the disease, while specificity refers to its ability to correctly identify those without the disease. The Positive Predictive Value (PPV) is the proportion of individuals with a positive screening test result who actually have the disease.
**Why the Correct Answer is Right**
To calculate the PPV, we first need to determine the number of individuals with the disease and the number of individuals without the disease in the population. Given that 20% of the population has the disease, we can calculate these numbers as follows:
- Number of individuals with the disease = 10,000 x 0.2 = 2,000
- Number of individuals without the disease = 10,000 - 2,000 = 8,000
Next, we need to calculate the number of true positives and false positives. Given the sensitivity and specificity of the screening test, we can calculate these as follows:
- True positives = Number of individuals with the disease x Sensitivity = 2,000 x 0.95 = 1,900
- False positives = Number of individuals without the disease x (1 - Specificity) = 8,000 x (1 - 0.8) = 1,600
Now, we can calculate the PPV as follows:
- PPV = True positives / (True positives + False positives) = 1,900 / (1,900 + 1,600) = 1,900 / 3,500 = 0.543 (rounded to 54%).
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not take into account the sensitivity and specificity of the screening test.
**Option B:** This option is incorrect because it is not the correct formula for calculating PPV.
**Option C:** This option is incorrect because it is not the correct calculation for the PPV.
**Clinical Pearl / High-Yield Fact**
When calculating PPV, it is essential to consider the sensitivity and specificity of the screening test, as well as the prevalence of the disease in the population. This is because PPV is highly dependent on these factors.
**Correct Answer:** A. 54%