Mammography has 90% sensitivity and 98% specificity for breast carcinova. What is the probability that woman with breast carcinoma remains un diagnosed 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 first need to understand the given data: mammography has a 90% sensitivity and a 98% specificity. The probability of a woman having breast carcinoma being diagnosed in a given year is 90%, which implies that the probability of her remaining undiagnosed in a given year is 10% (or 0.1). For her to remain undiagnosed for 2 consecutive years, we calculate the probability of both events happening: 0.1 * 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 2 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 C:** This option is incorrect for the same reason as Option A; it does not match the correct calculation.
- **Option D:** This option, , represents 1%, which matches our calculation but let's verify if it's the correct format for the answer.
## Clinical Pearl / High-Yield Fact
A key point to remember is that the negative predictive value (NPV) of a test, which is the probability that subjects with a negative screening test truly don't have the disease, depends on the prevalence of the disease and the test's specificity. However, the question here focuses on the probability of a false negative (or remaining undiagnosed) over consecutive tests, highlighting the importance of test sensitivity in serial testing scenarios.
## Correct Answer Line
**Correct Answer: D. 0.01**