It is not always meaningfull to use the disperson index to select a model. If you have time-to-event data, and summarize these data with number of events and number of personyears on each combination of covariates, then you can analyze the data with Poisson-regression. But, that is just a trick to make inference about parameters. In such case you can not use anykind of statistics that make use of the poisson-distribution, therefore you can also not use the dispersonindex and analyze the data with negative binomial instead. Even if you generate your own time-to-event data with piecewise-constant hazard-rates, and analyze with Poisson regegression you can observe a dispersion index far from 1. Even though that all assumptions for Poisson regression was fulfilled. The reason why the p-values can change so dramatically is that in the negative binomial distribution it involves a variance parameter. If your data is aggregated on one more covaraite (even that this covariate is not included in the model!) then the variance parameter will be much smaller, which in turns will make confidenceintervals more narrow and p-values smaller. I can illustrate the princip in this simple example: Let say you just have one covariate "a". then data mydata; input a count personyears; logpop=log(personyears); cards; 0 10 10 1 20 40 ; run; proc genmod data=mydata; class a; model count=a/dist=nb link=log offset=logpop; estimate 'a' a 1 -1; run; Now, same data, but in addition a covariate "b" is also observed and data is aggregated on "b" as well; data mydata; input a b count personyears; logpop=log(personyears); cards; 0 0 6 5 0 1 4 5 1 0 10 20 1 1 10 20 ; run; proc genmod data=mydata; class a; model count=a/dist=nb link=log offset=logpop; estimate 'a' a 1 -1; run; *with the negative binomial model you will get other p-values, but same mean estimates. *with Poisson you will get same results with the two models.;
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