The Book of Why: The New Science of Cause and Effect

by Judea Pearl

The diagram in Figure 6.4 encodes the crucial information that gender is unaffected by the drug and, in addition, gender affects the risk of heart attack (men being at greater risk) and whether the patient chooses to take Drug D. In the study, women clearly had a preference for taking Drug D and men preferred not to. Thus Gender is a confounder of Drug and Heart Attack. For an unbiased estimate of the effect of Drug on Heart Attack, we must adjust for the confounder. We can do that by looking at the data for men and women separately, then taking the average: FIGURE 6.4. Causal diagram for the Simpson’s paradox example. • For women, the rate of heart attacks was 5 percent without Drug D and 7.5 percent with Drug D. • For men, the rate of heart attacks was 30 percent without Drug D and 40 percent with. • Taking the average (because men and women are equally frequent in the general population), the rate of heart attacks without Drug D is 17.5 percent (the average of 5 and 30), and the rate with Drug D is 23.75 percent (the average of 7.5 and 40). This is the clear and unambiguous answer we were looking for. Drug D isn’t BBG, it’s BBB: bad for women, bad for women, and bad for people.