What is too much variation? The null hypothesis in small-area analysis.

A small-area analysis (SAA) in health services research often calculates surgery rates for several small areas, compares the largest rate to the smallest, notes that the difference is large, and attempts to explain this discrepancy as a function of service availability, physician practice styles, or other factors. SAAs are often difficult to interpret because there is little theoretical basis for determining how much variation would be expected under the null hypothesis that all of the small areas have similar underlying surgery rates and that the observed variation is due to chance. We developed a computer program to simulate the distribution of several commonly used descriptive statistics under the null hypothesis, and used it to examine the variability in rates among the counties of the state of Washington. The expected variability when the null hypothesis is true is surprisingly large, and becomes worse for procedures with low incidence, for smaller populations, when there is variability among the populations of the counties, and when readmissions are possible. The characteristics of four descriptive statistics were studied and compared. None was uniformly good, but the chi-square statistic had better performance than the others. When we reanalyzed five journal articles that presented sufficient data, the results were usually statistically significant. Since SAA research today is tending to deal with low-incidence events, smaller populations, and measures where readmissions are possible, more research is needed on the distribution of small-area statistics under the null hypothesis. New standards are proposed for the presentation of SAA results.