Question

Consider two medical tests, A and B for a virus. Test A is 90% effective at recognizing the virus when it is present, but has a 5% false positive rate. Test B is 80% effective at recognizing the virus when it is present, but only has a 1% false positive rate. The two tests are independent (i.e., they use different means for identifying the virus). The virus is carried by 2% of all people.

1) If you could use only one of the two tests to identify the virus, which would you choose? Justify your answer mathematically.

2) How much more certain can you be if you can use both tests?

Answer 1

1)

Test A

	Virus	Not Virus	Total	Ratio
Diagnosed	0.018	0.049	0.067	0.268657

Test B

	Virus	Not Virus	Total	Ratio
Diagnosed	0.016	0.0098	0.0258	0.620155

Hence Test B is more reliable.

2)

We will be more certain if we can use both test.

By combining we can obtain an optimal composite diagnostic test with higher sensitivity and specificity that detects the presence of the disease more accurately.

	Virus	Not Virus	Total	Ratio
Diagnosed	0.018	0.0098	0.0278	0.647482

Please revert back in case of any doubt.

Please upvote. Thanks in advance.