# Two rate chi squared tests infection rate

We would just like to display a crude statistic to compare infection rate pre/post intervention. Based on a paper I read the statistical test I need to apply is a 2 rate chi squared test. I've been looking for a tutorial but haven't been able to find something that I'm looking for.

                    MRSA Cases      Patient Days
Pre Intervention       61            102000
Post Intervention      41            110000


I have R and can do this in R if that's ideal.

• You'll need to say more for this to be answerable. Are the pre & post numbers on the sample people, eg? Are these hazard rates? What are your data, exactly? Apr 1 '15 at 18:57
• @gung thanks for your help. No the data is unit based. So comparing a medical unit pre/post and intervention. cid.oxfordjournals.org/content/45/7/901.long This is the paper where I got this information from. Apr 1 '15 at 19:04
• This is a test for equality of two Poisson means. One would have to hunt down the references to determine more precisely what test it is, since there are several (slightly different) ways to formulate such a test.
– whuber
Apr 1 '15 at 19:10

## 1 Answer

I gather you have two counts, and which could have been anything (i.e., they are not bounded—counts of successes out of a total number of trials). The simplest distribution of counts is the Poisson, but there can be other, more complicated, distributions as well (e.g., negative binomial). With your data, you cannot differentiate between different possible count distributions. You can assume they are Poisson, but that's it, and if that assumption is incorrect, your results will be invalid.

In addition, when people model counts, there is often a variable that indicates some kind of opportunity for an event to occur. That's what you have as "Patient Days", I gather. We adjust for this using an offset.

Thus, it is possible to have a (rather low powered) test of your data by assuming they are realized values from a single Poisson distribution and adjusting with an offset, and seeing if that looks reasonable. In R, this can be done with the ?poisson.test function:

poisson.test(x=c(61, 41), T=c(102000, 110000))
#
#   Comparison of Poisson rates
#
# data:  c(61, 41) time base: c(102000, 110000)
# count1 = 61, expected count1 = 49.075, p-value = 0.02222
# alternative hypothesis: true rate ratio is not equal to 1
# 95 percent confidence interval:
#  1.062580 2.445082
# sample estimates:
# rate ratio
#   1.604495

• Thanks gung appreciate this. We have some preliminary data and we suspect a change has occurred. I think it's time to constult a statistician to go through our data. Really appreciate this. Apr 1 '15 at 19:35