Testing the null hypothesis in small area analysis

The goal of small area analysis is often to demonstrate that hospital admission rates or procedure rates vary greatly among regions, suggesting the occurrence of unnecessary admissions or procedures in some regions. Recent articles have shown that such variation may be largely due to chance, even if no underlying differences exist among the small areas; thus, it is important to test if the observed variation is larger than expected by chance. In this article we discuss how the appropriate method for testing the null hypothesis depends on the distribution of the number of admissions at the person level. If it is not possible for an individual to have more than one admission for a given procedure, the appropriate test is a simple chi-square test. If multiple admissions are possible, a modified chi-square test can be used to account for the excess variability due to multiple admissions. Failure to make the correct modification to the chi-square test in this latter case can result in spurious results. This underscores the importance of collecting data on multiple admissions in order to estimate the distribution of the number of admissions at the individual-patient level.