Table 3.

Hypothetical data illustrating bias amplification. The conditional RD, which is the causal effect, is 0.10. The crude RD is −0.25, which translates into a bias of magnitude 0.35. The Z-adjusted RD is −0.11, which translates into a smaller bias of magnitude 0.21.

clinic	treatment	confounder
		U=0			U=1			U=?
		outcome			outcome			outcome
		Y=0	Y=1	pr(Y=1)	Y=0	Y=1	pr(Y=1)	Y=0	Y=1	pr(Y=1)
Z=0	X=0	240	60	0.20	20	180	0.90	260	240	0.48
	X=1	567	243	0.30	0	90	1.00	567	333	0.37
	RD			0.10			0.10			−0.11
Z=1	X=0	40	10	0.20	45	405	90	85	415	0.83
	X=1	28	12	0.30	0	60	1.00	28	72	0.72
	RD			0.10			0.10			−0.11
Z=?	X=0							345	655	0.655
	X=1							595	405	0.405
	RD									−0.25