A population of 1000 people in whom the prevalence of disease XYZ is 50%. ABC screening test was used to screen disease which has specificity and sensitivity of 50 %. What is positive predictive value of screening test ABC.
## Core Concept
The positive predictive value (PPV) of a screening test is the proportion of individuals with a positive test result who actually have the disease. It depends on the prevalence of the disease, the sensitivity, and the specificity of the test. The formula to calculate PPV is: PPV = (Prevalence * Sensitivity) / [(Prevalence * Sensitivity) + ((1 - Prevalence) * (1 - Specificity))].
## Why the Correct Answer is Right
Given that the prevalence of disease XYZ is 50% (or 0.5), the sensitivity of the ABC screening test is 50% (or 0.5), and the specificity is also 50% (or 0.5), we can substitute these values into the PPV formula. So, PPV = (0.5 * 0.5) / [(0.5 * 0.5) + ((1 - 0.5) * (1 - 0.5))] = 0.25 / (0.25 + 0.25) = 0.25 / 0.5 = 0.5 or 50%. This means that 50% of the individuals who test positive actually have the disease.
## Why Each Wrong Option is Incorrect
- **Option A:** This option is incorrect because it does not match our calculation of PPV.
- **Option B:** This option is incorrect for the same reason; the calculated PPV is 50%, not the value represented by this option.
- **Option D:** This option suggests a PPV of 25%, which would be incorrect based on our calculations.
## Clinical Pearl / High-Yield Fact
A key point to remember is that the PPV of a test is heavily influenced by the prevalence of the disease in the population being tested. A test with a sensitivity and specificity of 50% will have a PPV of 50% if the disease prevalence is 50%, as seen in this example. This relationship highlights the importance of considering the population's disease prevalence when interpreting test results.
## Correct Answer Line
**Correct Answer: C. 50%**