Risk ratio

The Risk Ratio is obtained by dividing the cumulative incidence of the exposed group (CI_e) by the cumulative incidence of the unexposed group (CI_u):

Risk Ratio = CI_e/ CI_u

Let us consider an example:

A study investigated the relationship between exposure to outdoor air pollution and development of respiratory illness in two cities, one of which (A) had significant outdoor air pollution, while the other city (B) did not have outdoor air pollution. The study followed up 1000 individuals over 10 years in each city. In city A, 400 of the 1000 study participants developed respiratory illnesses, while only 100 study participants developed respiratory illnesses in city B. The results of the study can be depicted in a 2×2 contingency table as:

Outdoor air pollution?	Respiratory illness	No respiratory illness	Total	Cumulative incidence
Yes	400	600	1000	400/1000 = 0.4
No	100	900	1000	100/1000 = 0.1

The risk of developing respiratory illness for those living in city A compared to the risk of developing respiratory illness for those living in city B is given by the Risk Ratio:

Risk Ratio = CI_e/ CI_u = 0.4/0.1 = 4.0

Interpretation: Those living in city A had 4.0 time the risk of developing respiratory illness due to outdoor pollution compared to those living in city B.

Caution: The risk ratio of 4.0 is in comparison to the baseline risk (here living in city B). it is incorrect to interpret the risk ratio as ‘Those living in city A had 4 times greater risk’ or ‘Those living in city A had 4 times more risk’. When we say 4 times greater risk, we are saying 400% higher risk. However, the excess risk for those living in city A is (4-1) *100 = 300%. (We subtract 1 as that is the baseline risk- the risk of those living in city B). One could say ‘Those living in city A had 4.0 times the risk of respiratory illness compared to those living in city B’ as a correct interpretation of the results.

When the Risk Ratio >1, % increase = (Risk Ratio – 1)* 100

When the Risk Ratio <1, % decrease = (1- Risk Ratio)* 100

You may have noticed that we have not considered the time element inherent in incidence rate, just the cumulative incidence.