For statistics LOVERS - a tough USMLE scenario to discuss

[SCME500]

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I recently stumbled across a stats question that I did not answer correctly. Can anyone please help and explain it to me?

This was a question from one of the big question banks, so I will modify it but obviously if you really are good at stats you will get it:

"When a patient takes The HIV Truth Test and picks 2 of 4 responses as positive, chances that he has HIV are 100%. Last bill unanimously passed by the government prior to the mid-term elections required that 3 out of 4 responses be positive to label the patient as HIV-positive. What is the effect of this bill on sensitivity and specificity?

Now I am reasonably good with stats and I know that raising the bar to "label the patient as HIV+" means increased specificity and therefore decreased specificity.

What threw me off was the "100%" part. I thought that "chances that he has HIV 100%" means that the test is 100% sensitive and 100% specific. The explanation does not touch this issue at all. So hope one of you can help.



Thanks. 😕

 

[mrmandrake]

I'm not great at stats but I'll give my take on it.

"I thought that "chances that he has HIV 100%" means that the test is 100% sensitive and 100% specific."

I don't think this is true. It would only mean that the test is 100% specific, meaning if you answer 2 out of 4 you have HIV. It is not 100% sensitive because it doesn't mention that everyone with HIV will answer 2 out of 4.

The effect of raising the bar to 3 out of 4 will not change the specificity since everyone who answers 3 out of 4 will have HIV. It does change the sensitivity because those who answer 2 out of 4 will be missed by the new law even though they have HIV.

Someone feel free to correct me if I'm wrong.

Edit: I was wrong about the test being 100% specific. It is not as explained by the guys below.

I recently stumbled across a stats question that I did not answer correctly. Can anyone please help and explain it to me?

This was a question from one of the big question banks, so I will modify it but obviously if you really are good at stats you will get it:

"When a patient takes The HIV Truth Test and picks 2 of 4 responses as positive, chances that he has HIV are 100%. Last bill unanimously passed by the government prior to the mid-term elections required that 3 out of 4 responses be positive to label the patient as HIV-positive. What is the effect of this bill on sensitivity and specificity?

Now I am reasonably good with stats and I know that raising the bar to "label the patient as HIV+" means increased specificity and therefore decreased specificity.

What threw me off was the "100%" part. I thought that "chances that he has HIV 100%" means that the test is 100% sensitive and 100% specific. The explanation does not touch this issue at all. So hope one of you can help.



Thanks. 😕

 

[kstreet]

I recently stumbled across a stats question that I did not answer correctly. Can anyone please help and explain it to me?

This was a question from one of the big question banks, so I will modify it but obviously if you really are good at stats you will get it:

"When a patient takes The HIV Truth Test and picks 2 of 4 responses as positive, chances that he has HIV are 100%. Last bill unanimously passed by the government prior to the mid-term elections required that 3 out of 4 responses be positive to label the patient as HIV-positive. What is the effect of this bill on sensitivity and specificity?

Now I am reasonably good with stats and I know that raising the bar to "label the patient as HIV+" means increased specificity and therefore decreased specificity.

What threw me off was the "100%" part. I thought that "chances that he has HIV 100%" means that the test is 100% sensitive and 100% specific. The explanation does not touch this issue at all. So hope one of you can help.



Thanks. 😕

Wait what?

Can you rephrase?

 

[qmcat]

I think the new test has increased specificity and decreased sensitivity. That means the new test will pick up less people, but the people that the test does pick up are more likely to be HIV+. So there are less false positives with the new method.

 

[PlAnEjaNe]

I think the new test has increased specificity and decreased sensitivity. That means the new test will pick up less people, but the people that the test does pick up are more likely to be HIV+. So there are less false positives with the new method.

Exactly this 👍

Whenever you change the parameters of a test to make it 'more difficult' to get a positive (i.e. they need to meet more criteria or stricter criteria) then the specificity is increased but the sensitivity is decreased. Just think about what the old classifications for diabetes was...it used to be something like 160 (or maybe it was 140...whatever you get what I mean) fb glucose was a positive for diabetes but they lowered that number to 126 so they decreased specificity but increased sensitivity, meaning they would pick up a whole hell of a lot more positives that might not be diabetic but at least they would pick up all the ones that really were diabetic, whereas the old criteria picked up mostly diabetics (not too many false positives) but also missed a lot of diabetics that didn't meet the criteria (lots of false negatives!). So the change was implemented to pick up all the diabetics and who cares if some are false positives because, what the hell, they probably need lifestyle changes and diet modification anyways.

 

[SCME500]

Wait what?

Can you rephrase?

i think that my wording is equivalent to the ambiguity that the original question had. but the question is not about the direction of movement and what happens with sensitivity/specificity... i have no problems figuring out that the specificity would go up and sensitivity down in a similarly worded question, for example glucose measurements, etc.... i only have a problem with the "100% chance" issue.

i do not agree with the answers given above because "and picks 2 of 4 responses as positive, chances that he has HIV are 100%" means that THE POSITIVE PREDICTIVE VALUE IS 100%. with it comes the rest... the FP rate is therefore 0%. The specificity is ALREADY a 100%. it cannot increase anymore.

in my opinion, the answer can be specificity remains unchanged, sensitivity goes down (which is not an answer choice).

care to explain/ponder more? hope so. thanks.

 

[SCME500]

I'm not great at stats but I'll give my take on it.

"I thought that "chances that he has HIV 100%" means that the test is 100% sensitive and 100% specific."

I don't think this is true. It would only mean that the test is 100% specific, meaning if you answer 2 out of 4 you have HIV. It is not 100% sensitive because it doesn't mention that everyone with HIV will answer 2 out of 4.

The effect of raising the bar to 3 out of 4 will not change the specificity since everyone who answers 3 out of 4 will have HIV. It does change the sensitivity because those who answer 2 out of 4 will be missed by the new law even though they have HIV.

Someone feel free to correct me if I'm wrong.

Edit: I was wrong about the test being 100% specific. It is not as explained by the guys below.

sorry, i did not see your first answer. i do believe that you are right. the answers after you only discuss similarly worded questions that require you to say that sp/sens will go down/up and dont mention the "100% chance" part that i believe changes this question a little bit. i think that this means that the specificity of the test is 100% to start of with becuase the FP rate is 0%. (PPV is 100%). 👍

 

[PlAnEjaNe]

sorry, i did not see your first answer. i do believe that you are right. the answers after you only discuss similarly worded questions that require you to say that sp/sens will go down/up and dont mention the "100% chance" part that i believe changes this question a little bit. i think that this means that the specificity of the test is 100% to start of with becuase the FP rate is 0%. (PPV is 100%). 👍

Oh yes, I completely missed that part
so I guess the correct answer would read something like:
"specificity remains unchanged while sensitivity is further decreased"

 

[mrmandrake]

Thanks haha. I think I'm right but whoever posts next will probably convince me that I'm wrong.

sorry, i did not see your first answer. i do believe that you are right. the answers after you only discuss similarly worded questions that require you to say that sp/sens will go down/up and dont mention the "100% chance" part that i believe changes this question a little bit. i think that this means that the specificity of the test is 100% to start of with becuase the FP rate is 0%. (PPV is 100%). 👍

 

[SCME500]

Thanks haha. I think I'm right but whoever posts next will probably convince me that I'm wrong.

👍