ing bias in ecologic studies is quite difficult in practice. Nevertheless, certain design features tend to reduce ecologic bias, including the following:

  1. 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.

  2. 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.

  3. Exposure should be as uniform as possible within groups but as different as possible between groups.

  4. 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.

  1. 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).

  2. 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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