problem set 4- questions 5 f) and g)

problem set 4- questions 5 f) and g)

by Chloe Kern -

Hello,

I'm having trouble understanding what questions 5 f) and g) of problem set #4 are asking and was hoping for some help to frame the problem correctly. The way I'm understanding the problem now is that we should be using threshold probability to determine whether we would use the test in question (x-ray) exclusively or resort to two gold-standard tests, knowing the that this would result in double gold-standard bias. However I don't quite understand how to tie this all together. Do you have any suggestions for how I should be framing these questions?

Thank you!
Chloe

Re: problem set 4- questions 5 f) and g)

by Michael Kohn -

Hi Chloe,

My colleagues may consider this too big of a hint, but this is a reward to anybody who reads the Forum.

If you are willing to do 20 x-rays to find 1 elbow fracture, then you should x-ray anybody with a probability of elbow fracture greater than 1/20 = 5%.  The index test in this question is the elbow extension test, but right now we are talking about doing an x-ray, which for purposes of this problem, is a perfect but costly test, and T = B/20.  See Ch 2, page 27.

Back to the elbow extension test.  The decision it is supposed to guide is whether to get an x-ray.  Remember, we said tests guide "treatment" decisions, but sometimes "treatment" is just getting another test, in this case, an x-ray.  

We just saw that the threshold probability Ptt for getting an x-ray is 5%.  If you start with a pre-test probability similar to that observed in this study (>> 5%), will a negative elbow extension test allow you to skip the x-ray?  Does it matter whether you use the potentially biased estimates of sensitivity and specificity versus the "true" values?

MAK


Re: problem set 4- questions 5 f) and g)

by Chloe Kern -

That makes a lot more sense, thank you!

Re: problem set 4- questions 5 f) and g)

by Michael Kohn -

Sorry, if I confused things.  If it is worth doing 20 x-rays to diagnose 1 fracture, then you should x-ray anyone with a probability of fracture > 1/20 = 5%.  If it is worth doing 50 x-rays to diagnose 1 fracture, then your Ptt = 2%.

Apparently my earlier post made some people who were doing the problem correctly think that they were doing it wrong.  They looked at 1 - NPV, which for Part C was 1.6% and for Part D was 3.5%.  This is post-test probability after a negative test.  If your treatment threshold is 5%, then it doesn't matter whether you use the numbers from Part C or D.  A negative elbow extension test allows you to skip the x-ray.   But if your treatment threshold is 2%, then it does matter.  If you use the numbers from Part D, a negative elbow extension test does NOT allow you to skip the x-ray.