A test was considered for diagnosing a disease. Out of 80 positive cases with this test, 40 actually had no disease. Out of 9920 tested negative cases 9840 actually had no disease. Calculate the sensitivity of the test –
**Core Concept**
The sensitivity of a diagnostic test measures its ability to correctly identify those with the disease, calculated as the number of true positive results divided by the sum of true positive and false negative results. In this context, we're evaluating the test's performance in detecting the disease.
**Why the Correct Answer is Right**
To calculate sensitivity, we need to identify the true positive and false negative cases. Out of 80 positive cases, 40 actually had no disease, which means 40 are false positives. Since 40 out of 80 positive cases are false positives, the remaining 40 positive cases are true positives. With 9920 tested negative cases, 9840 had no disease, leaving 80 true negative cases. However, to calculate sensitivity, we need to know the total number of actual disease cases. We can infer that the number of actual disease cases is 40 (false positives) + x (true positives), where x is the number of true positives. Since the total number of positive test results is 80, we can calculate sensitivity as the number of true positives divided by the sum of true positives and false negatives. However, the question asks for sensitivity, which is the ratio of true positives to the sum of true positives and false negatives. Given that we do not have the exact number of false negatives, we can use the given information to calculate the sensitivity as the number of true positives divided by the total number of actual disease cases.
**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect as it doesn't involve the calculation of true positives and false negatives in the context of sensitivity.
* **Option B:** This option is incorrect as it doesn't provide a clear calculation for sensitivity.
* **Option C:** This option is incorrect as it doesn't consider the total number of actual disease cases.
* **Option D:** This option is incorrect as it doesn't provide a clear calculation for sensitivity.
**Clinical Pearl / High-Yield Fact**
When calculating sensitivity, it's essential to understand that it measures the test's ability to correctly identify those with the disease, not the ability to correctly identify those without the disease. This distinction is crucial in evaluating the performance of diagnostic tests.
**Correct Answer: B. 40/40 = 1.**