How to compare two incidence ratios statistically- the rate parameter test I want to compare two standardized incidence ratios (SIR) obtained in stratified analyses. I read in Mocci et al (2013) that they used the rate parameter test and cited the book Statistical models in epidemiology by Clayton and Hills. 
I can't find anything else online and don't want to pay to buy the book. Does anyone know and can elaborate on this? 
 A: You can use a R package called popEpi (available in CRAN) to calculate confidence intervals for the ratio of two SIRs. Here is an example where I assume that the observed (o1 and o2) and expected (e1 and e2) cases known:
library(popEpi)
# observed and expected cases of the First SIR
o1 <- 12
e1 <- 10

# observed and expected cases of the Second SIR
o2 <- 14
e2 <- 10


sir_ratio(x = c(o1, e1), y = c(o2, e2))

> sir_ratio     lower     upper 
>     0.857     0.362     1.997 

sir_ratio refers to the book Statistics with Confidence: Confidence Intervals and Statistical Guidelines, Douglas Altman. The method is also explained in the help page of the sir_ratio. Note that the ratio of two SIRs might give biased results if e.g. the age structures in both SIRs are very different (more about that see Breslow & Day, 1987). 
You can also test whether the two SIRs are equal using a likelihood ratio test of two nested Poisson regression models. However this will only give you a p-value. You can check functions sir and sir_exp from popEpi for LRT.
