Question

4. In epidemiology, the population attributable risk is heuristically defined as AR-NP(E)[P(DIE)-P(DIE)] NP(D) where N is the size of the population, D is the event of being a sick person with the disease under investigation, and E is the event of being a person exposed to the risk factor of interest. (4.1) Interpret the meaning of AR by interpreting the meanings of conditional probabilities in the above definition. (4.2) Prove thaRE P(D)

Answer 1

4.1

N * P(E) = Number of exposed persons to the risk in the population

N * P(D) = Number of sick persons with the disease

N * P(D) / N * P(E) = Rate of sick persons in exposed

P(D | E) = Probability of disease for exposed persons

P(D | E^c) = Probability of disease for unexposed persons

P(D | E) - P(D | E^c) = Difference in probabilities of disease between exposed and unexposed persons

Thus, AR can be interpreted as difference in probabilities of disease between exposed and unexposed persons divided by the rate of disease among exposed.

4.2

NP(D) P(D)

P(D)

P(E)PDE (1-P(E)P DES P(D)

P(D)

{By law of total probability, P(D) = P(E)P(D | E) + P(E^c)P(D | E^c) }

P(D) - P(DE) P(D)