Population is 10,000, of these 20% having disease. The screening test has 95% sensitivity and 80% specificity. PPV is –
The question gives a population of 10,000 with 20% prevalence. That means 2,000 have the disease and 8,000 don't. The test has 95% sensitivity and 80% specificity. To calculate PPV, I need to use a contingency table. True positives would be 95% of 2,000, which is 1,900. False negatives are the remaining 100. For the non-diseased group, specificity is 80%, so true negatives are 80% of 8,000 = 6,400. False positives are 20% of 8,000 = 1,600. Total positives are TP + FP = 1,900 + 1,600 = 3,500. So PPV is 1,900 / 3,500 ≈ 54.29%.
Now, the correct answer should be around 54%. The options aren't provided, but the user mentioned the correct answer is . So I need to make sure the explanation is thorough. For the wrong options, common mistakes might involve using prevalence alone or confusing PPV with sensitivity. Also, some might miscalculate the numbers leading to incorrect percentages. The clinical pearl here is that PPV is highly dependent on disease prevalence, so in low prevalence, even a good test can have low PPV. That's a key point for exams.
**Core Concept**
Positive Predictive Value (PPV) is the probability that a person with a positive test result truly has the disease. It depends on **test sensitivity, specificity**, and **prevalence** of the disease in the population.
**Why the Correct Answer is Right**
In a population of 10,000 with 20% prevalence (2,000 diseased), **95% sensitivity** means 95% of the 2,000 (1,900) test positive (true positives). **80% specificity** means 80% of the 8,000 non-diseased (6,400) test negative (true negatives), leaving 20% (1,600) as false positives. Total positive tests = 1,900 (TP) + 1,600 (FP) = 3,500. **PPV = TP / (TP + FP) = 1,900 / 3,500 ≈ 54.29%**.
**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect if it assumes PPV equals sensitivity (95%), ignoring prevalence and specificity.
**Option B:** Incorrect if it uses specificity (80%) directly without calculating true positives/false positives.
**Option C:** Incorrect if it calculates **negative predictive value