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?
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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. – Stephan Kolassa Dec 05 '21 at 13:04
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You can't even do it if you know n. – Mitch Dec 05 '21 at 14:33
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Look here at the start, under 'traditional approach'. – BruceET Dec 05 '21 at 17:07
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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.
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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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