How to determine the accuracy of three combined tests

[mjolnir91]

Hypothetically, I have three tests that can determine if someone has cancer or doesn't have cancer. A True positive would indicate that the person doesn't have cancer. Below is a description of each test.

Test 1: TP=.7 , FN = .3 , FP= .1 , TN = .9 , Accuracy = 80%
Test 2: TP=.8 , FN = .2 , FP= .2 , TN = .8 , Accuracy = 80%
Test 3: TP=.6 , FN = .4 , FP= .47 , TN = .53 , Accuracy = 56.5%

(TP = true positive, FN = false negative, FP = false positive, TN = true negative)

What calculation can be done to determine how certain one could be that someone has cancer given that all three tests indicate the patient has cancer?

 

[Dason]

Seems like you would want to use Baye's theorem for this. Do you know the prevalence of this type of cancer in the general population?

 

[mjolnir91]

I've used bayes theorem already the problem is if you say 85% of all people don't have cancer and 15% do have cancer. Than even if all three tests indicate that the person has cancer the probability that the individual has cancer conditioned on the fact that all three tests say he has cancer is like 1.5%. Which makes the tests seem entirely pointless to me. If three tests say someone has cancer and the chance of him actually having it is only 1.5% why bother with the tests at all.

Unless my math is off it seems like there has got to be a better way to describe to someone how confident they can be in the assessment given by the three tests.