Figure 4.

Confounding by group, illustrating Table 2. A) Individual level: The solid black lines describing the individual-level information in the two groups are parallel (same risk differences b) but have different intercepts (different background risks q₀ ≠ q₁). The crude estimate of the risk difference b_c is confounded (blue line). B) Group level: The ecologic estimate of the risk difference b_e is the slope of the red line through the two ecologic data points. Massive confounding has occurred, but we can't tell this from the ecologic data alone. C) Comparison of results on the two levels: The ecologic estimate of the risk difference b_e is much more biased than the crude individual-level estimate b_c. Both biases are in the same direction.