Quiz HN: Test your biases

4 points·jibiki··7 comments

You are the minister of health. Currently, you screen all citizens for cow-flu using test X. You want to add another test, though, and you have two options: test Y or test Z. Test Y is strongly correlated with test X. Test Z is not correlated with test X.

Do you add test Y or test Z?

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Please provide more information. What is the specificity of each test? What is the sensitivity of each test? And how virulent is the disease? And how expensive is each test?

http://en.wikipedia.org/wiki/Sensitivity_and_specificity

http://www.nhhealthcost.org/costByProcedure.aspx

That's pretty much the right answer.

Let's say all tests cost the same and are 99% specific. Test X is at least 70% sensitive. Test Y and Z have unknown sensitivity.

All good tests should be strongly correlated with the presence/absence of swine flue, and hence correlated with each other. So either tests X/Y are broken, or test Z is broken. Or both.

We need to figure out which before answering the question.

Let's say X and Y are both good tests. Is it still possible you would prefer Z to Y?

If Z caught most of the cases that X missed, but not many that X caught then it would be very useful.

My first instinct is to add test Z. Since Y correlates well with X, Z would provide more information.

But if Y is correlated to X, that might indicate something about its sensitivity.

If there are tests for a binary result (has cow-flu/does not have cow-flu) that are not correlated, one or both of the tests is bad. Further information could confirm or negate the choice of Y or Z (or sticking only with X).

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