# Calculating confidence interval for multiple groups of risk ratios

#### cgn

##### New Member
I have a question regarding calculating confidence intervals (95%) in SAS for multiple exposure groups (with one being the reference group). The numbers below represent the number of people who were exposed versus the number of people who became ill along with the cum incidence, sickness rate and risk ratio.
I calculated the following risk ratios by hand with the 18 - 29 group being the reference group and I have the following questions:

- Is it possible to calculate confidence intervals for multiple exposure groups? If so what would that process be?
- Would I input the table below in order to calculate the confidence intervals in a statistical program, or would the risk ratios and confidence intervals have to be calculated in using the raw data? Is is possible to calculate by hand (or is there a calculator)?

#### katxt

##### Well-Known Member
Is it possible to calculate confidence intervals for multiple exposure groups? If so what would that process be?
Just to be clear, are you looking for the 95% CIs for the numbers in the "risk ratio" column? kat

#### hlsmith

##### Less is more. Stay pure. Stay poor.
In SAS you could get these with PROC FREQ approach with the "/ RELRISK" option in the Table statement or do it by hand.

Standard error and interval formulae are as follows:

se_rate<-sqrt((b/(a*(a+b)))+(d/(c*(c+d))))

lower_cl<-RR*exp(-1.96*se_rate)
upper_cl<-RR*exp(1.96*se_rate)

Of note, you may want to change the alpha to correct for repeated comparisons, so you would substitute the (-)1.96 for a larger number to help minimize type I errors.