topic Need proof of the distribution of a incidence rate (e.g., xx events per yy person-years) in New SAS User

Need proof of the distribution of a incidence rate (e.g., xx events per yy person-years)

TomHsiung — Sat, 07 Jun 2025 07:20:55 GMT

Hello, guys

I am thinking why the incidence rate could be treated as a nearly normally distributed parameter.

We know that the central limit theorem enables us to treat parameters like mean and risk as approximately normally distributed. How about incidence rate? It looks like the incidence rate is not a form of mean so we cannot directly apply the central limit theorem to it.

I know there is the proc stdrate to estimate the incidence rate, very nice. But I just want to dig deeper, to understand the statistic behind. Thank you.

Tom

Re: Need proof of the distribution of a incidence rate (e.g., xx events per yy person-years)

MarkusWeick — Mon, 09 Jun 2025 07:56:43 GMT

Hi @TomHsiung, for a start have a look at the Poisson Distribution (https://en.wikipedia.org/wiki/Poisson_distribution). It is the standard for independend (!) events.

Best

Markus

Re: Need proof of the distribution of a incidence rate (e.g., xx events per yy person-years)

Ksharp — Mon, 09 Jun 2025 08:10:53 GMT

If the rate's pointed estimate(mean of rate) was near 0.5 , then you could take it as a normal distribution.
But if it was near 0 or 1,that could not be normal distribution.
This has been discussed at other post by @Rick_SAS

And as other said ,you could use Poisson Distribution to build a model about rate:
https://support.sas.com/kb/24/188.html