Insights on bias and information in group-level studies

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Abstract
Ecological and aggregate data studies are examples of group‐level studies. Even though the link between the predictors and outcomes is not preserved in these studies, inference about individual‐level exposure effects is often a goal. The disconnection between the level of inference and the level of analysis expands the array of potential biases that can invalidate the inference from group‐level studies. While several sources of bias, specifically due to measurement error and confounding, may be more complex in group‐level studies, two sources of bias, cross‐level and model specification bias, are a direct consequence of the disconnection. With the goal of aligning inference from individual versus group‐level studies, I discuss the interplay between exposure and study design. I specify the additional assumptions necessary for valid inference, specifically that the between‐ and within‐group exposure effects are equal. Then cross‐level inference is possible. However, all the information in the group‐level analysis comes from between‐group comparisons. Models where the group‐level analysis provides even a small percentage of information about the within‐group exposure effect are most susceptible to model specification bias. Model specification bias can be even more serious when the group‐level model isn't derived from an individual‐level model.

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