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Fluoride in Drinking Water: A Scientific Review of EPA’S Standards Appendix C Ecologic and Partially Ecologic Studies in Epidemiology Individual-level studies collect information on outcome, exposure, and covariates (potential confounders and effect modifiers) for each individual. Ecologic studies collect information about groups. Partially ecologic studies use a combination of individual-level and group-level variables. The goal of most ecologic studies is to make inferences about individuals based on aggregated data. Unfortunately, severe bias can occur. (Bias in this context means systematic errors in the results of the analysis; it does not impugn the integrity or intention of the researchers). Ecologic bias has several sources (Greenland 1992; Greenland and Robins 1994; Morgenstern 1998; Webster 2000): Nondifferential exposure misclassification within groups (which tends to bias results away from the null) Confounding within and between groups Effect measure modification within and between groups Misspecification error when model is nonlinear Inadequate control of covariates Magnification of bias by aggregation due to confounding by group and effect measure modification by group Failure to weight by population Failure to standardize both outcome and exposure in the same way. Instead of simply dismissing all ecologic studies as unreliable, it is preferable to estimate the direction and magnitude of potential biases. Quantify-
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Fluoride in Drinking Water: A Scientific Review of EPA’S Standards ing bias in ecologic studies is quite difficult in practice. Nevertheless, certain design features tend to reduce ecologic bias, including the following: Studies with outcome variables that can be modeled with weighted or ordinary least-squares regression (e.g., bone fluoride levels) are generally preferable to those with binary outcomes or rates, commonly modeled with logistic or log-linear regression. Nonlinear ecologic models can induce bias due to misspecification. Exposure variables that are continuous on the individual-level before aggregation are generally preferable to those that are dichotomous (aggregation of dichotomous exposures typically produces variables of the form “fraction exposed”). The latter can be subject to nondifferential exposure misclassification within groups, tending to bias ecologic studies away from the null; they also tend to increase the amount of bias magnification. In contrast, using of the average exposure within each group need not cause measurement error on the ecologic level, a special case of the Berkson error model. Errors of this type produce unbiased results in ordinary linear regression; in log-linear regression, bias also depends on variance of the errors. Exposure should be as uniform as possible within groups but as different as possible between groups. Avoid, if possible, confounders with highly nonlinear relationships to outcome, because these can be very difficult to control in ecologic studies. The following two types of partially ecologic studies are often used in epidemiology. Multilevel models typically supplement individual-level variables with contextual variables. The latter are intrinsically group-level variables that have no real counterpart on the individual-level, (e.g., herd immunity or income inequality). Studies that measure outcome and covariates at the individual level, but exposure at the group level, are commonly used in environmental and occupational epidemiology. This design is sometimes called “semi-individual.” For example, fluoride concentrations might be measured in the water system serving a community. Everyone in that group is assigned the same exposure. Exposure is an aggregated variable, not an intrinsically group-level variable. Feasibility is the typical reason for using this design; individual exposure measurements are typically expensive and time-consuming, if they are possible at all. The semi-individual kind of partially ecologic study can be thought of as individual-level with exposure measurement error. Unfortunately, semi-individual studies are not necessarily free of ecologic bias. Suppose the
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Fluoride in Drinking Water: A Scientific Review of EPA’S Standards ecologic exposure variable is the fraction exposed in the group (aggregated from dichotomous exposures at the individual level). Nondifferential exposure misclassification within groups tends to produce bias away from the null as in ecologic studies. Although bias magnification (see list above) can occur, the amount of bias tends to be intermediate between a fully ecologic study and a fully individual study (at least in certain cases that have been analyzed). Because covariate information is collected at the individual level, the ability to control for confounding can be much better than with purely ecologic studies. For more discussions of these issues, see Webster (2000, 2002) and Björk and Strömberg (2002). In sum, semi-individual studies are generally more trustworthy than fully ecologic studies. Studies using exposure variables based on continuous individual-level exposures are preferable to those based on dichotomous individual-level exposures.
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