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# RE: st: Difference between two age-specific incidence rates and IRR following Poisson regression

 From Tim Evans To statalist Subject RE: st: Difference between two age-specific incidence rates and IRR following Poisson regression Date Mon, 1 Oct 2012 13:58:10 +0100

```Peng,

Thanks for your reply and suggestion. I think I have realised that the reasons for the differences are a little more subtle. Firstly my age-specific rates are interested in those who had a maj surgery compared to the general population, whereas the Poisson regression is not interested in the general population (not included in model) but is interested in the number of cases who did not have a maj surgery. There are differential rates of increase in population size, cohort size and surgery (with regards to maj/minor) in the cohort. While the proportion of surgery has increased, the proportion of maj surgery compared to overall surgery has fallen in the later period. I'm still trying to get my head around it, but think I'm getting there now.

Best wishes

Tim

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of smztsmzt
Sent: 01 October 2012 13:40
To: statalist
Subject: Re: st: Difference between two age-specific incidence rates and IRR following Poisson regression

Hi Tim,

You could have a look at
the “Incidence Rate Ratio Interpretation” in
http://www.ats.ucla.edu/stat/stata/output/stata_poisson_output.htm. It might be useful for you.

Best wishes,

Peng

2012-10-01

Hi all,

I hope you may be able to help.

I am looking at the age specific incidence rates of a type of surgery in cancer patients in a given age group over set periods in time. I have then run a simple Poisson regression model to assess the incidence rate ratio between a base period and following periods in time using the same age group.

So for instance.

One set of data I find the following:

major surgery rate per 100,000 people in 1988-89 is 73.5 (in the 50-59 age group)
major surgery rate per 100,000 people in 2008-10 is 96.1 (in the 50-59 age group)

If I calculate the rate ratio of 2008-10 to 1988-89 from the data above I have a ratio of 1.31

If I calculate the IRR using Poisson regression for the same data, I return a value of 0.86 (CIs 0.79, 0.93) - which I am clearly finding hard to explain.

The age-specific incidence rates are calculated by dividing the count of surgeries in the given population group and multiplied by 100,000. The poisson regression code in Stata looks like this:

poisson maj_surg flag2 if age=="50-59", irr

maj_surg is binary 0 = no major surgery, 1 = major surgery
flag5 is binary 0 = 1988-89, 1 = 2008-10

The major surgery rates calculated above are age specific calculations, whereas the IRR calculated (although based upon the same age groups) are not necessarily, but as I'm presenting age specific results, this is surely not an area of difference.

Are the difference related to the fact that my age-specific rates do not take account of any underlying distribution of the data whereas I am implicitly saying in the Poisson regression calculation that the data have a Poisson distribution, and as such the underlying calculations are going to be different?

Any pointers really appreciated.

Best wishes

Tim

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