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

by Judea Pearl

In 1946, Joseph Berkson, a biostatistician at the Mayo Clinic, pointed out a peculiarity of observational studies conducted in a hospital setting: even if two diseases have no relation to each other in the general population, they can appear to be associated among patients in a hospital. To understand Berkson’s observation, let’s start with a causal diagram (Figure 6.3). It’s also helpful to think of a very extreme possibility: neither Disease 1 nor Disease 2 is ordinarily severe enough to cause hospitalization, but the combination is. In this case, we would expect Disease 1 to be highly correlated with Disease 2 in the hospitalized population. FIGURE 6.3. Causal diagram for Berkson’s paradox. By performing a study on patients who are hospitalized, we are controlling for Hospitalization. As we know, conditioning on a collider creates a spurious association between Disease 1 and Disease 2. In many of our previous examples the association was negative because of the explain-away effect, but here it is positive because both diseases have to be present for hospitalization (not just one). However, for a long time epidemiologists refused to believe in this possibility. They still didn’t believe it in 1979, when David Sackett of McMaster University, an expert on all sorts of statistical bias, provided strong evidence that Berkson’s paradox is real. In one example (see Table 6.3), he studied two groups of diseases: respiratory and bone. About 7.5 percent of people in the general p...