Mammography has 90% sensitivity and 98% specificity for breast carcinona. What is the probability that a woman with breast carcinoma remains undiagnosed for 2 consecutive years?
## **Core Concept**
The problem involves understanding the concepts of sensitivity and specificity of a diagnostic test, in this case, mammography for breast carcinoma. Sensitivity refers to the test's ability to correctly identify those with the disease (true positive rate), while specificity refers to the test's ability to correctly identify those without the disease (true negative rate).
## **Why the Correct Answer is Right**
To find the probability that a woman with breast carcinoma remains undiagnosed for 2 consecutive years, we need to calculate the probability of a false negative result for two consecutive years. Given that the sensitivity of mammography is 90%, the probability of a false negative result (i.e., missing a case of breast carcinoma) in one year is (1 - 0.9 = 0.1) or 10%. For two consecutive years, the probability of remaining undiagnosed is ((0.1) times (0.1) = 0.01) or 1%.
## **Why Each Wrong Option is Incorrect**
- **Option A:** This option is incorrect because it does not accurately reflect the calculation for the probability of remaining undiagnosed for two consecutive years based on the given sensitivity and specificity.
- **Option B:** This option suggests a higher probability than calculated, which does not align with the correct calculation of 1%.
- **Option D:** This option suggests a much higher probability than calculated, which is incorrect.
## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the effectiveness of screening tests like mammography is highly dependent on their sensitivity and specificity. A 90% sensitivity and 98% specificity for mammography indicate a high level of accuracy, but no test is perfect. Understanding the limitations of these tests is crucial for interpreting results and making clinical decisions.
## **Correct Answer:** C. 0.01