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I have the sensitivity value known as, 0.825 and specificity as 1.00. Can we derive the True Positive (TP) and True Negative (TN) values from that? Is that possible at all?

Kabir Guglani
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  • Is this a question from a course or textbook? If so, please add the [tag:self-study] tag & read its [wiki](https://stats.stackexchange.com/tags/self-study/info). – Stephan Kolassa Dec 05 '21 at 13:04
  • You can't even do it if you know n. – Mitch Dec 05 '21 at 14:33
  • Look [here](https://stats.stackexchange.com/questions/455129/trying-to-estimate-disease-prevalence-from-fragmentary-test-results) at the start, under 'traditional approach'. – BruceET Dec 05 '21 at 17:07

1 Answers1

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Sensitivity is $\text{TP}/(\text{TP+FN})$, and specificity is $\text{TN}/(\text{TN+FP})$. If specificity is $1$, there is no false positives. The sensitivity figure yields $0.175\times\text{TP}=0.825\times \text{FN}$.

Even if you know the total number of samples, $\text{TP+FN+TN}=n$, you'd still need to know the number of true negatives in terms of others. So, it's not possible to calculate the true pos/neg.

gunes
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  • like this is the question what do you think they are asking, I am a little confused. "Emma took a rapid antigen test for SARS-CoV-2 and her test came out positive. The particular brand of antigen test that she used claims that in their clinical study, the test showed a sensitivity of 0.825 and a specificity of 1.00. Assuming that their claimed numbers are true and given that she has been tested positive, what is the probability that she is actually positive for SARS-CoV-2?" – Kabir Guglani Dec 05 '21 at 20:59
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    this question asks for a probability, not the actual TP or TN – gunes Dec 05 '21 at 21:09
  • But how do I calculate it that's not what I am understanding? – Kabir Guglani Dec 05 '21 at 21:20
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    you should use Bayes rule – gunes Dec 05 '21 at 21:27
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    thanks for your help. – Kabir Guglani Dec 05 '21 at 21:33
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    @KabirGuglani you’re welcome – gunes Dec 05 '21 at 21:34
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/132084/discussion-between-kabir-guglani-and-gunes). – Kabir Guglani Dec 05 '21 at 22:35