Sensitivity of a diagnostic test

Mia30

New Member
There is an exercise that I am not able to solve: Diagnostic tests A1 and A2 are used to detect the presence or absence of a disease. The results of A1 and A2 are a priori independent of the presence or absence of the disease. A1 and A2 have sensitivity Sen1 and Sen2, respectively. A new diagnostic test T is introduced. T is positive when A1 and A2 are both positive. Determine the sensitivity of T.

Initially, I thought I would use Bayes theorem, as it contains sensitivity and re-arranging the equation I would get the sensitvity of T: P(Test+│D)=P(D│Test+)*(P(test+│D)*P(D)+P(test+│notD)*P(notD))/P(D)

But since there are no numbers behind, I don´t know how to solve this problem..

any help is highly appreciated!

katxt

Active Member
The "numbers" are Sen1 and Sen2.
I suspect that you are overthinking the problem.
The sensitivity of T is the probability of a positive given that the patient has the disease and T is positive when A1 and A2 are both positive. So, what is the probability that A1 and A2 will both be positive given that the patient has the disease?

Mia30

New Member
Thank you Katxt! I indeed have! you just put me on the right track, thanks so much!