Comparing Standardized Rates of Events

This paper reviews issues associated with testing a null hypothesis of the equality of, and generating descriptive statistics for, standardized rates of events--recurrent or non-recurrent. The variance estimation for rates of surgical procedures, hospitalizations, and health care expenditures is discussed in the context of small area analysis. The proposed approach for estimating the variance of standardized rates is independent of assumptions about the underlying distribution of rates, is widely applicable, and seems preferable to approaches derived under special, but uncertain, parametric assumptions. A statistic is suggested based on person-level data, which allows comparing both rates of events and variation in rates between independent groups. The proposed statistic does not depend on the underlying unknown distribution of the events and does not require restrictive assumptions such as equal variances among the competing rates.