# Calculate confidence interval from point estimate and standard error

Im having a problem with calculating a confidence interval for an incidence rate ratio between two populations. Using PROC STDRATE from SAS, I've obtained the Incidence Rate Ratio (the difference in incidence rate between two time periods), the log rate ratio, the standard error and the z-value.

I wonder (1) why on earth did SAS not provide confidence intervals for the rate ratio? (2) How can I myself calculate these?

But this is not a mean, which is why the simple formula: SE = SD/√(sample size), probably isnt correct.

Many thanks in advance for help!

They do give you a standard error and a $z$ value, which suggests that the SAS developers thought it reasonable to use the normal distribution to approximate the sampling distribution of the statistic involved. So, if you can confirm that your $z$ statistic is equal to the estimated log rate ratio (call it $LRR$) divided by the standard error, then I would be comfortable in using $LRR \pm 2\times SE$ as an approximate 95% CI for the true log rate ratio. Supposing that this results in an interval $(\ell,u)$, then the interval $(e^\ell, e^u)$ provides a 95% CI for the incidence rate ratio itself.
• NO - leave it negative! $e^x$ is still positive when $x<0$. – rvl Jul 30 '14 at 16:31