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 2×2 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 $n\cdot p\cdot (1-p) \ge 5$)
Best Answer
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.
As @onestop pointed out in their comment methods of calculating a binomial proportion confidence interval can be used here. The method you follow is the normal approximation, however unless you have really large counts other methods like the Wilson interval will be more accurate.