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# Confidence intervals for rates using Poisson distribution

I am trying to calculate Poisson-based 95% confidence intervals for rates. Is there a way to do this in SAS? The rates are based on small numbers of events, so the standard normal-based 95% CIs aren't appropriate.

Thanks.

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‎07-06-2017 10:12 AM
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## Re: Confidence intervals for rates using Poisson distribution

See this usage note that discusses the modeling or rates and computing rate estimates and confidence limits:

http://support.sas.com/kb/24188

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## Re: Confidence intervals for rates using Poisson distribution

Would you describe your problem with a little more detail? You speak of rates, so that leads me to believe that you have differing exposure time for different observations. But it would be good to know more precisely what data you have and what you want to estimate.
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## Re: Confidence intervals for rates using Poisson distribution

We are using birth and population data to calculate birth rates. The confidence intervals will be used to compare rates by time intervals and locations.
Regular Contributor
Posts: 171

## Re: Confidence intervals for rates using Poisson distribution

Assuming that the data are distributed as Poisson conditional on the population size, then you can obtain confidence intervals for the Poisson rate using the GENMOD procedure as follows:

proc genmod data=mydata;
model birth_count = / dist=poisson offset=log_PopSize;
estimate "log(rate)" intercept 1;
run;

where log_PopSize is the (natural) log of the population size and birth_count should be self explanatory. The above code would provide the rate for a population of size 1. You probably don't want to specify the rate for a population of size 1. In order to specify the rate for a population of size K, compute log_PopSize as

log_PopSize = log(PopSize / K);

Of course, the variable log_PopSize needs to be constructed before executing the GENMOD procedure. You might also want to examine whether a negative binomial distribution specification provides a better fit than the Poisson.
Solution
‎07-06-2017 10:12 AM
SAS Employee
Posts: 306