took this further to decompose the overall distribution of suicide rates into a mixture of two Poisson distributions, the first to characterize the normal rate and the second to characterize the elevated rate, possibly due to one or more “suicide epidemics.” When they fit the model to 10 years (1977–1987) of monthly suicide rate data from Cook County (Chicago area), they found no evidence for a contribution of the second distribution. However, as described in Appendix A, using this analysis on the spatial distribution of suicide has identified qualitatively distinct geographic groupings of suicide rates across the United States. During the past decade, statistical research on finite mixture distributions has developed greatly (for review, see Böhning, 1999) and holds great promise for application to suicide. Appendix A describes the general statistical theory and developments.
In the analysis of suicide rate data, Poisson regression models are a natural choice. With this approach, the data are modeled as Poisson counts whose means are expressed as a function of covariates. For example, the data may consist of yearly county-level suicide rates, broken down by age, sex, and race for that year. For these type of rate estimates a fixed-effects model is usually used. When there is a mixture of fixed (e.g., age, sex, and race) and random effects (e.g., unobservable county-specific effects), the more general mixed-effects Poisson regression model is used. In the case of suicide, the rates are considered to be nested within geographic locations (e.g., counties) and can represent multiple rates obtained over time (e.g., yearly suicide rates for a given county) or rates for different strata within a given county (e.g., males and females) or both. The random effects would modify the rate for each county from the population average.
Often, it is of interest to estimate values of the random effects within a sample. In the present context, these estimates would represent the deviation of the suicide rate for a given county from the national mean suicide rate, conditional on model covariates such as age, race, and sex, which may be either fixed or random effects. This can be done by using an empirical Bayes estimator of cluster-specific effects.6 Thomas et al. (1992)