topic Re: Negative Binomial and Incidence in Statistical Procedures

Negative Binomial and Incidence

EpiNovice — Thu, 07 Nov 2019 03:34:11 GMT

Hi everyone:

I'd like to calculate incidence rates. I know it can be done using Proc GENMOD with Poisson and lsmeans, however my data is over-dispersed and it looks like negative binomial is the way I need to go. Is there a way to calculate incidence using negative binomial in Proc GENMOD?

My variables are as follows:

Events: dependent variable, gives a count of events per 1000 person days
Disease: predictor variable, yes/no
Days: days of follow-up

I'd like the incidence for the whole group as well as stratified by disease status. Suggestions?

Thanks in advance!

Re: Negative Binomial and Incidence

unison — Fri, 08 Nov 2019 01:02:09 GMT

Take a look here: https://stats.idre.ucla.edu/sas/dae/negative-binomial-regression/

There is an example of using proc genmod with a negative binomial distribution

...

proc genmod data = nb_data;
  class prog (param=ref ref=first);
  model daysabs = math prog / type3 dist=negbin;
run;

...

-unison

Re: Negative Binomial and Incidence

StatDave — Fri, 08 Nov 2019 14:57:52 GMT

That is done in exactly the same way as with a Poisson model as discussed in this note. Simply change the response distribution in GENMOD to DIST=NEGBIN. Otherwise, use the same LSMEANS statement.

Re: Negative Binomial and Incidence

JacobSimonsen — Sat, 09 Nov 2019 20:18:59 GMT

My suggestion is to use the poisson regression model - no matter whether you see overdisperson or not.

The reason for that that overdispersion is something that measure variance relative to mean for count-data. But here the data was time-to-event, which has been summarized by number of events and person-time. It can be analyzed with poisson regression assuming piecewice constant incidence rates, because the likelihood function for will be similar to what you would have if you assumed the count-data was poisson distributed. As you dont need the assumption of distribution it you also dont need to check for overdispersion.

It quite easy to simulate time to event data with some incidence rate, and estimate the incidencerate with confidence interval correctly, even that you may have a big over dispersion. The dispersion will depend on how much you have aggreated (for example 5 agegroup instead of 10), which can be completely arbitrary and irrelevant for the rate estimate and it std error. So, just use proc genmod with the dist=poisson, and remember the offset=logtime.