12. Suppose that events A and B are that people have diseases a and

b, respectively. Suppose that having either disease leads to hospitalization H = A ∪ B. If A and B are believed to be independent events, show that P(A|BH) < P(A|H).

Thus if hospital populations are compared, a spurious negative association between A and B might be found. This is called Berkson’s Paradox (Berkson (1946)).