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I have the sensitivity value known as, 91%. Can we derive the True Positive (TP) and True Negative (TN) values from that. Is that possible at all?

Thanks.

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    $\begingroup$ No. All you know is that $\dfrac{TP}{TP+FN}=0.91$ so one equation and two unknowns. Perhaps you also know $TP+TN +FP+FN=1$ so two equations and four unknowns $\endgroup$
    – Henry
    Jul 12, 2017 at 23:41

2 Answers 2

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If the only thing you know is the sensitivity, the answer is no. Even if you know the total population this sensitivity was calculated in, the answer is still no. Because the sensitivity calculation only contains information about the TP and FN. You still have the unaccounted false positives and true negatives. You need more information to be able to calculate these.

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  • $\begingroup$ Thanks for your answer. I also have the specificity and accuracy values, would that help me at all? $\endgroup$
    – Simplicity
    Jul 13, 2017 at 22:37
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    $\begingroup$ Someone should correct me if I'm wrong, but I'm pretty you also need the prevalence (so what percentage actually has the outcome) and total population to be able to calculate this. Then: FP = (1 - Specificity) * (1 - Prevalence); TN = Specificity * (1 - Prevalence); TP = Sensitivity * Prevalence; FN = (1 - Sensitivity) * Prevalence. These formulas give a fraction, which you'll then have to multiply with the total population to get the exact TP and TN values. $\endgroup$
    – Tami
    Jul 14, 2017 at 7:41
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Someone should correct me if I'm wrong, but I'm pretty you also need the prevalence (so what percentage actually has the outcome) and total population to be able to calculate this. Then: FP = (1 - Specificity) * (1 - Prevalence); TN = Specificity * (1 - Prevalence); TP = Sensitivity * Prevalence; FN = (1 - Sensitivity) * Prevalence. These formulas give a fraction, which you'll then have to multiply with the total population to get the exact TP and TN values.

ans: it is not correct way of calculation, I tested with many original values, all are incorrect output.

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