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I am trying to compare incidence rate ratios (IRR). This is what I have:

Group A (exposed vs. unexposed) IRR and Group B (exposed vs. unexposed) IRR

So how would I correctly test for the difference between the IRR from Group A and the IRR from Group B? The question I would like to answer is whether the incremental differences observed in Group A are similar to those observed in Group B? Please help!

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    $\begingroup$ Sec. 6.3 of Agresti 2002 (2nd ed.) discusses some options, including the CMH test mentioned by @JamesStanley If you are an R user you may find the R/S companion to this book helpful, specifically p.102 sec E. The R function mantelhaen.test runs the CMH test. $\endgroup$
    – conjugateprior
    Commented Feb 1, 2013 at 11:42
  • $\begingroup$ Oops. That was more of an answer than I was intending. Perhaps @James-Stanley wants to incorporate it into his. $\endgroup$
    – conjugateprior
    Commented Feb 1, 2013 at 11:44

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Generally speaking, you could either apply a Mantel-Haenszel test for whether the impact of the exposure factor differs between groups A and B (basically a stratified chi-squared test), or almost equivalently, model with Poisson regression and include an interaction term between exposure and group status to test whether these differ (EDIT: I mean whether exposure differs by group here too)

Wikipedia is (for once) not very verbose on this subject, but does give a two-liner summary. http://en.wikipedia.org/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics

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