Assuming that mammography has a sensitivity of 90 percent and a specificity of 98 percent, and that consecutive tests are independent, what is the probability that a woman with breast cancer will have a negative screening mammogram for two consecutive years? (AIIMS Nov 2012)
a. The multiplicative rule applies to independent events.
b. The probability of a negative test if there is cancer can be expressed as P (T — / D +) and is equal to 1 — sensitivity (1 — 0.9 = 0.1), or the false negative rate.
c. The probability of two negative consecutive tests is (0.l) (0.1) = 0.01 = 1 / 100. The probability that a woman who has cancer will test negative decreases with the number of mammographies done. This is inherent to the sensitivity of the test.
d. The higher the sensitivity, the lower the probability of false negative tests as they are repeated.