# What does the decomposition of a relative risk look like?

Say I have a relative risk of smokers that smoked 1-20 cigarettes per day. What is the mathematical identity between that RR, the RR of those that smoked 1-10 cig/day, and RR of those that smoked 11-20 cig/day, all with the same reference group? I tried decomposing it for RR's and kept getting stuck. Basically I am trying to figure out what the functions for the below would look like.

$$RR_{all} = f(RR_1) + g(RR_2)+c$$

• I don't think there can exist any such identity: don't you also need information about the sizes of these subgroups? – whuber Mar 1 '19 at 17:35