I am trying to run what should be a straightforward Poisson regression to obtain adjusted mortality rates at county-level. I must first clarify that my issue is not about choosing between a marginal (GEE) vs. subject-specific model. My data consists of the following variables: y=death counts, Ni=population at risk, sex=(M/F), Agegrp=3 age groups, and other covariates: x1=% of educated (at county level), x2=% of employed (at county level). My aim is to obtain Mortality rates/100,000 at county level based on the model consisting of the explanatory variables as shown below:
I am aiming to fit the following Poisson regression model (with an offset log(Ni) :
log(lambda_i)= bo + b1*Agegrp + b2*Sex + b3*X1 + b4*X2 + ui
where ui=county random effects.
I tried following the example from SAS help using random effects model fitted using PROC GLIMMIX (v9.4). This approach seems to do the trick, but the problem is the rates I am getting are not at county-level but rather at the level of the explanatory variables. Is there a way I could obtain these at county level? At the end I want to rank these counties by the adjusted mortality rates from the Poisson regression. Fitting a marginal mode (GEE) did not help either. I would welcome any suggestions.
The code is as below:
PROC GLIMMIX DATA=mydata;
CLASS county;
MODEL deaths = agegrp sex X1 X2 / DIST=poisson OFFSET=log_Ni S DDFM=Satterth;
RANDOM county;
My_Rate= 100000*exp(_zgamma_ + _xbeta_);
ID county deaths pop My_Rate;
OUTPUT OUT=got_you;
RUN;
Thank you Haris, I much appreciate your suggestion. I was not sure I was doing the correct thing, but as you suggested, indeed what I need are the random intercepts.
Thanks once more for the clarification it is very helpful. I was struggling/confused a bit about the correct interpretation of the random effects. You understood me correctly, it's much clearer now. For example in my case with 2-levels of hierarchy in my data, it would be enough as I am seeking differences from the national (aka sample) average in this case. It then makes sense again if I had an additional level, say e.g. Districts, then the random effects at this level will represent differences from county average.
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