Bias magnification in ecologic studies: a methodological investigation

BACKGROUND: As ecologic studies are often inexpensive to conduct, consideration of the magnitude and direction of ecologic biases may be useful in both study design and sensitivity analysis of results. This paper examines three types of ecologic bias: confounding by group, effect measure modification by group, and non-differential exposure misclassification. METHODS: Bias of the risk difference on the individual and ecologic levels are compared using two-by-two tables, simple equations, and risk diagrams. Risk diagrams provide a convenient way to simultaneously display information from both levels. RESULTS: Confounding by group and effect measure modification by group act in the same direction on the individual and group levels, but have larger impact on the latter. The reduction in exposure variance caused by aggregation magnifies the individual level bias due to ignoring groups. For some studies, the magnification factor can be calculated from the ecologic data alone. Small magnification factors indicate little bias beyond that occurring at the individual level. Aggregation is also responsible for the different impacts of non-differential exposure misclassification on individual and ecologic studies. CONCLUSION: The analytical tools developed here are useful in analyzing ecologic bias. The concept of bias magnification may be helpful in designing ecologic studies and performing sensitivity analysis of their results.