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 2x2 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.
- 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?