# How do you compute confidence intervals for positive predictive value?

How do you compute confidence intervals for positive predictive value?

The standard error is:

$$SE = \sqrt{ \frac{PPV(1-PPV)}{TP+FP}}$$

Is that right? (here my concern is the denominator)

Does that formula work for any similar ratio in a 2x2 table. E.g. for sensitivity, it would be

$$SE = \sqrt{ \frac{SENS(1-SENS)}{FP+TN}}$$

Is that right? (here my concern is that it is generalizable to other ratios as long as you get the denominator right)

And the for the 95% confidence intervals:

$$CI_{PPV} = PPV \pm 1.96*SE$$

Is that right? (my concern here is how to go from SE to the confidence interval)

(of course with all the cell restrictions like $n\cdot p\cdot (1-p) \ge 5$)

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Thanks for the link. My question is if I am getting $n$, the denominator, right for the different variations (and confirmation that the other instances are right). –  Mitch Apr 11 '11 at 21:12
This related question might be useful, Statistical test for Positive and Negative Predictive Value. –  chl Apr 12 '11 at 10:15
Your first SE formula is correct. The second SE formula which concerns sensitivity should have the total number of positive cases in the denominator: $$SE_\text{sensitivity} = \sqrt{ \frac{SENS(1-SENS)}{TP+FN}}$$
The logic is that sensitivity = $\frac{TP}{TP+FN}$, and the denominator in the SE formula is the same.