The Book of Why: The New Science of Cause and Effect (Penguin Science)

by Judea Pearl

Cornfield took direct aim at Fisher’s constitutional hypothesis, and he did so on Fisher’s own turf: mathematics. Suppose, he argued, that there is a confounding factor, such as a smoking gene, that completely accounts for the cancer risk of smokers. If smokers have nine times the risk of developing lung cancer, the confounding factor needs to be at least nine times more common in smokers to explain the difference in risk. Think of what this means. If 11 percent of nonsmokers have the “smoking gene,” then 99 percent of the smokers would have to have it. And if even 12 percent of nonsmokers happen to have the cancer gene, then it becomes mathematically impossible for the cancer gene to account fully for the association between smoking and cancer. To biologists, this argument, called Cornfield’s inequality, reduced Fisher’s constitutional hypothesis to smoking ruins.