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Show Estimates for small samples can be stabilized using empirical Bayes (EB) statistical estimation procedures (Devine, Annest, & Kirk, et al.). An EB method developed by Manton et al. (1989, as cited in Devine, Annest, & Kirk, et al.) develops a stabilized age-specific rate for each area that is a weighted average of two components: the age-specific rate observed in the area, and the age-specific rate estimated for that area on the basis of the observed rates of all areas ("prior probabilities"). In areas with large populations, the stabilized EB rate gives more weight to the observed rate for that area. For areas with smaller population sizes, the weight on the observed rate tends to decrease, and the modified EB rate moves closer to the rate estimated from the other areas, thus smoothing, but not flattening, the dramatic peaks and valleys that are evident on trend lines for small areas. Bayesian smoothing, itself, does not identify statistically significant differences in the data. In fact, the Bayes-adjusted data tend to underestimate the true variance that is found in the observed population rates (Martuzzi and Elliott, 1996). Specialized methods are required for calculation of confidence or "credibility" intervals and other statistics on EB stabilized data (Greenland & Robins, 1991). Although the result of this method, "smoothing" of improbable extreme values, is appealing, the method itself requires more statistical expertise than the methods previously discussed, and may not be practical for those desiring a quick solution. Ecological Fallacy. A well-documented problem with the interpretation of data from small area analyses, commonly referred to as "ecological fallacy", is that of using aggregate (i.e., small area) data to represent associations at an individual level (International Epidemiological Association, 1995). Associations found between variables at the small area level will sometimes disappear or even reverse when recomputed with data at the individual level. In addition, associations may change depending on the spatial boundaries used. Statistical techniques have been developed to attempt to adjust for the bias resulting from the ecological fallacy problem, allowing inferences to be made about individual associations (King, 1998). As with other types of data, care must be taken when interpreting associations to avoid making inappropriate inferences. Synthetic Estimation. Another analytic technique that is relevant to the analysis of small area information is synthetic estimation, used to estimate the value of some rate or measure in a small area where it has not been directly measured. In synthetic estimation, the observed relationships between predictor variables, typically demographic characteristics such as age, sex, race, and an outcome variable in a standard population, such as a state or U.S. population, are applied to known demographic characteristics in the small area to produce an estimate of the outcome variable in the small area (Lafata, Koch and Wiessert, 1994). Synthetic estimates can be useful for small area planning in the absence of direct local estimates; however, one must be willing to accept the untestable assumption that the relationships between predictor and outcome variables found in the standard population will hold true in the small area. Even if the relationships between variables generalize to other populations, synthetic estimation can only account for whatever variation in health variables is attributable to variation in the sociodemographic variables used in the analysis (Spasoff et al., 1996). Mapping Deciding Which Characteristics to Map. A decision must be made regarding which aspect of the health event to display spatially: the place of residence of the individual, the place of the incident, the place of the exposure, or the place where the health service was rendered. Although this is an important consideration from the standpoint of the research question, it is often a moot point because data are usually only available according to one of the above schemes. However, persons who are creating new data reporting systems, or making refinements to existing systems should consider geocoding the data in more than one way to allow for more flexibility in the use of the data. Deciding How to Display the Information. Maps can be a powerful communication tool, communicating the size and shape of an area, its location and neighbors on a single page. Several issues confront the investigator in this process. Information may be presented by shading blocks of areas (chloropleth map), such as a map of the U.S. with states in varying shades of some hue or density of gray to signify differences on some variable. Information may also be presented by plotting points (isopleth map), for instance, plotting each individual case of a communicable disease according to the residence of each victim (Kirby, 1996). If blocks are to be used, will the shading variations of the blocks represent ranges of values assumed by the variable of interest, ranges of percentiles on the variable of interest, or 24 |
