Table 3.

Effect modification of the risk difference by group

	Group 0			Group 1			Crude
	expose	unexpose	sum	expose	unexpose	sum	expose	unexpose	sum
case	20	10	30	48	12	60	68	22	90
noncase	80	90	170	32	108	140	112	198	310
total	100	100	200	80	120	200	180	220	400
risk	0.2	0.1		0.6	0.1		0.378	0.1
RD	0.1			0.5			0.278
X i	0.5			0.4
Y i	0.15			0.3
n i	200			200

The background risks in each group are the same but the risk differences vary. The crude individual-level risk difference lies between the two extremes, as it must when exposure is binary. The ecologic estimate of the risk difference, (Y₁-Y₀)/(X₁-X₀)= -1.5, is extremely biased. RD = risk difference; X_i and Y_i are the average exposure and average risk in group i; n_i = size of group i.