Odds ratio and relative risk (see Figure on page 1690 of Zhang and Yu):
(1) If the incidence of an outcome in the study population is < 10%, then the odds ratio is close to the risk ratio.
(2) As the incidence of the outcome increases, the odds ratio overestimates the relative risk if it is more than 1, or underestimates the relative risk is less than 1.
Situations when desirable to perform correction:
(1) if the incidence of the outcome in the nonexposed population is more than 10%, AND
(2) if the odds ratio is > 2.5 or < 0.5
incidence of outcome in nonexposed group = N =
= (number with outcome in nonexposed group) / (number in nonexposed group)
incidence of outcome in exposed group = E =
= (number with outcome in exposed group) / (number in exposed group)
risk ratio =
= E / N
odds ratio =
= (E / (1 - E)) / (N / (1 - N))
E / N =
= (odds ratio) / [(1 - N) + (N * (odds ratio))]
corrected risk ratio =
= (odds ratio) / [(1 - N) + (N * (odds ratio))]
This equation can be used to correct the adjusted odds ratio obtained from logistic regression.
