Doriangray

Number needed to diagnose

10 posts in this topic

Came across a question on the paper b recall thread (oct 15).

From what was said, appeared that the following data was given about a test:

sensitivity: 59%

specificity: 80%

 

asked how many would need to be screened to get 250 correctly diagnosed individuals.

Just wanted to check if my logic on this is correct.

1. of every 100 persons with the disease, 59 + (TP) and 41 - (FN)

     of every 100 persons without the disease, 20 + (FP) and 80 - (TN)

2. so it takes 200 persons tested to get 59 true positives.

3. it takes 200/59 to get one true positive

4. it takes (200/59)*250 to get 250 true positives.

Would that work?

 

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oh just realised thre's a fatal flaw in this. without knowing the relative prevalences of those with/without the disease, this cannot be calculated. am letting it stand so that someone can give full information on the question, if they remember it.

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Is the question asking for likelihood ratio of being positive? 

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Hi Doriangray,

I found this question very similar:

 

If sensitivity 76% and specificity 81%, how many patients with the disease needs to be screened using the test, to correctly identify 250 subjects?

Answer  329

 

As sensitivity - 76%- is the number of true positives among the diseased, in order to correctly diagnose 76 diseased patients, the test should be applied to 100 patients in total.

To diagnose 250 subjects correctly, we have to screen (250/76) X 100 in total.

We need to test 329 patients, to correctly identify 250.

 

So with this reasoning in your question the answer would be 424 patients (423.72)

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Er I'm not so sure, honestly.

Let's say you test x subjects in your example. without knowing their disease status. some p*x will have the disease, (1-p)*x will not (where p is the prevalence).

Of those p*x persons, the test will identify p*sensitivity*x persons. 

so p*sensitivity*x is the number would identify, which you know is 250

so rather than 329, it would be 250/(p*sensitivity) that you'd need.

My method initially assumed that there were equal numbers with and without the disease (because i just took 100 and 100, which was WRONG)

but assuming that were so, p would be 0.5. It would then work out that it's 250/(0.59*0.5) which returns to 500/0.59, ie 847.

For your example, again assuming 0.5 is the prevalence, it would be 250/(0.5*0.76), ie 658 (1/0.5 times your number).

So basically in your method, it would have to be inflated by 1/p, and without prevalence, the calculation can't be done. is what i think.

Edited by Doriangray

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That question belongs to spmm mock and they explaining it in that way. 

I consider prevalence wouldn't necessary in this case. 

Edited by Carole

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Ah well, no way to clear that up, then. :-)

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Good question! You are both correct, because your questions are slightly different.

Dorian it is impossible to answer your question exactly without prevalence. The answer would be greater that 250/.8 and less than 250/.59

But if you are asking just how many positives out of those with the disease then it is simply N/Sensitivity

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On 07/04/2016 at 10:23, Everest said:

Hi Doriangray,

I found this question very similar:

 

If sensitivity 76% and specificity 81%, how many patients with the disease needs to be screened using the test, to correctly identify 250 subjects?

Answer  329

 

As sensitivity - 76%- is the number of true positives among the diseased, in order to correctly diagnose 76 diseased patients, the test should be applied to 100 patients in total.

To diagnose 250 subjects correctly, we have to screen (250/76) X 100 in total.

We need to test 329 patients, to correctly identify 250.

 

So with this reasoning in your question the answer would be 424 patients (423.72)

 

 

424 would be number of patients with the disease. not the total number of the sample

On 07/04/2016 at 10:57, Doriangray said:

Er I'm not so sure, honestly.

Let's say you test x subjects in your example. without knowing their disease status. some p*x will have the disease, (1-p)*x will not (where p is the prevalence).

Of those p*x persons, the test will identify p*sensitivity*x persons. 

so p*sensitivity*x is the number would identify, which you know is 250

so rather than 329, it would be 250/(p*sensitivity) that you'd need.

My method initially assumed that there were equal numbers with and without the disease (because i just took 100 and 100, which was WRONG)

but assuming that were so, p would be 0.5. It would then work out that it's 250/(0.59*0.5) which returns to 500/0.59, ie 847.

For your example, again assuming 0.5 is the prevalence, it would be 250/(0.5*0.76), ie 658 (1/0.5 times your number).

So basically in your method, it would have to be inflated by 1/p, and without prevalence, the calculation can't be done. is what i think.

yes to get the total sample number we wld require a prevalence rate. 424/prevalence rate

On 07/04/2016 at 06:04, Doriangray said:

Came across a question on the paper b recall thread (oct 15).

From what was said, appeared that the following data was given about a test:

sensitivity: 59%

specificity: 80%

 

asked how many would need to be screened to get 250 correctly diagnosed individuals.

Just wanted to check if my logic on this is correct.

1. of every 100 persons with the disease, 59 + (TP) and 41 - (FN)

     of every 100 persons without the disease, 20 + (FP) and 80 - (TN)

2. so it takes 200 persons tested to get 59 true positives.

3. it takes 200/59 to get one true positive

4. it takes (200/59)*250 to get 250 true positives.

Would that work?

 

how many would yyou need to screen is asking about the sample size

Edited by luyi fada
completion

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