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

Abstract

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 intrvals relate more closely to some standard rate ratio estimators than standard exact intervals. yet they are morc tlificult to calculnte. We introduce an approximation to estimatc 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 nor111a1 method as the counts and personyears increase at the same rate. We compare our approximation to the exact DSR int,ervals and show by sin~ulating some cases with non-proportiollwl popl~ lations that the approximation is usually slightly more conservative than the exact DSR intervals. Comparing other known approximation in the same manner. we show that these other intervals are often more liberal than the exact DSR intervals.