Approximate confidence intervals for rate ratios from directly standardized rates with sparse data

We consider a class of exact confidence intervals for rate ratio (or relative risk) estimators calculated with directly standardized rates (DSRs) assuming a multiplicative Poisson model, which we call "exact DSR intervals". These intervals relate more closely to some standard rate ratio estimators than standard exact intervals, yet they are more difficult to calculate. We introduce an approximation to estimate these intervals using the inverse F distribution. We show that the approximation is equivalent to both types of exact intervals when the standard is proportional to both populations and is asymptotically equivalent to the log transformed normal method as the counts and person-years increase at the same rate. We compare our approximation to the exact DSR intervals and show by simulating some cases with non-proportional populations that the approximation is usually slightly more conservative than the exact DSR intervals. Comparing other known approximations in the same manner, we show that these other intervals are often more liberal than the exact DSR intervals.