I believe the solution by @JacobSimonsen could be helpful to my analysis. I am analyzing the number of procedures done by a Fellow each year (count) from 2008 to 2017 with an offset for the number of admissions in that year (lnAdmissions), dependent variables include the type of procedure (cateogircal; 1,2,3) and the number of years since 2008 (my time variable). I am also analyzing the interaction between procedure*time because there is a hypothesis that each type of procedure affects the rate differently over time. When running poisson: proc genmod data = longSummary order=data;
class procedure;
model count = yearsSince2008 procedure procedure*yearsSince2008 / dist=poisson type3 offset=lnAdmissions link=log ;
title "Poisson regression with offset and interaction";
run;title; footnote; I am faced with the (deviance value / DF) = 4 which suggests overdispersion of the data. I have also seen from multiple sources that as lambda increases, the variability of the data increases so there is no surprise this is showing overdispersion. I was inclined to go with the negative binomial route for accounting for overdispersed data - this does result in lower AIC and does not change any conclusions for the type 3 p values. My question is does my data fit the statement you made : It is wrong to apply the neg-bin distribution to this kind of data - even if you see a significant overdispersion when applying the Poisson option. The reason for this is that the data doesn't need to be Poisson distributed. Actually, the data which is behind your number of events is time-to-event data. If the assumption of piecewise constant rates are fulfilled, then data can be analyzed by poisson regression. Any help/suggestions would be greatly appreciated.
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