Confidence Intervals for Standardized Mortality Ratios

When measuring the quality of a hospital by event rates of certain indications or after specific treatment, it is important to perform a
risk adjustment in order to account for the fact that different hospitals see patients that systematically differ in their characteristics,
such as age or pre-existing health conditions. One way to summarize the hospital results over such strata is the computation of standardized
mortality (or morbidity) ratios (SMRs).

To take into account statistical effects, SMRs are often reported with confidence intervals.  These confidence intervals are usually obtained
under various approximations.  For small ratios, Poisson confidence intervals can be obtained.  When the confounding risk factors vary
only little among patients, binomial confidence intervals (exact or Wilson) can be used.  Asymptotic confidence intervals based on the
normal distribution have also been proposed.

We follow an approach by Clay and compute exact confidence intervals for SMRs based on the Poisson binomial distribution. We compare the
coverage of such intervals with existing procedures.