Let D denote having a certain disease and E denote having exposure to a certain risk factor. The attributable risk (AR) is the proportion of disease cases attributable to that exposure (see Benichou...

Let D denote having a certain disease and E denote having exposure to a certain risk factor. The attributable risk (AR) is the proportion of disease cases attributable to that exposure (see Benichou 1998).

a. Let P(E) = 1 — P(E). Explain why

AR= [P(D) — P(D|E)/P(D).

b. Show that AR relates to the relative risk RR by

AR = [P(E)(RR —1]/[1 + P(E)(RR — 1)] .