# Multinomial logistic regression: Interpretation of odds ratios as relative risks

In the context of an epidemiological study, a multinomial regression analysis was used to obtain odds ratios for an outcome variable with four different categories.

proc logistic data=ha8  descending;
class gp    (ref='1')/ param=ref;
run;


For example we got results as follows (the values are fictional):

• 1.4 is the multinomial logit estimate for a one unit increase in BMI (continuous) for group 4 relative to group 1. If a subject were to increase his BMI by one point, the multinomial log-odds for group 4 relative to group 1 would be expected to increase by 40%.
• 1.3 is the multinomial logit estimate for a one unit increase in BMI (continuous) for group 3 relative to group 1. If a subject were to increase his BMI by one point, the multinomial log-odds for group 3 relative to group 1 would be expected to increase by 30%.
• 1.2 is the multinomial logit estimate for a one unit increase in BMI (continuous) for group 2 relative to group 1. If a subject were to increase his BMI by one point, the multinomial log-odds for group 2 relative to group 1 would be expected to increase by 20%.

Which conditions are necessary in order to interpret odds ratios obtained from this multinomial logistic regression, as relative risks?

Many thanks!