I want to calculate the 95% CI for an incidence rate ratio (IRR), but I only have incidence rates per 10,000. (I do not have counts for the 2×2 table.)
Specifically, the incident rates were previously calculated by dividing passively monitored infection counts by the catchment area population (subset by the appropriate subpopulation) multiplied by 10,000.
Thus:
- Incidence rate A = 7.86 per 10,000
- Incidence rate B = 0.58 per 10,000
- IRR = A/B = 13.56.
The Katz log approach often used to compute CIs for odds ratios and rate ratios doesn't seem to apply here, because it is expecting counts, not ratios, to compute the standard error (in log space):
log(SE) = sqrt(1/a + 1/b – 1/m – 1/n),
where a and b are the successes for the two groups and m and n are the totals.
However, I can easily calculate the proportions (i.e. p-hat(A) = 7.86/10,000 = 0.000786).
Can I calculate the log(SE) from the proportions instead of the counts?
Thanks!!!
Best Answer
You need to have some sort of absolute count or error on the rate to get a confidence interval.
Imagine you had rates of 1/1000. The confidence interval would have to depend on whether you made 1 observation in 1000 samples of 10 in 10000 samples. If you just have the rate (0.001), the confidence is exactly information you don't know.
Do you have some sort of error on the rates calculated? Why can't you go back to the counts?