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I am trying to run an adjusted poisson regression in SAS using our existing data.

The model is: # of cases of disease= years + screening of disease rate. I am using an offset = log(total population).

My issues lie in the fact that when using YEAR as my primary independent variable and adjusting for another variable (screening rate), there are not enough degrees of freedom. I have 7 years (observation level) of data, so when I try to adjust for the screening rates the screening rate variable has no estimate value.

any thoughts on how to get by this or another way to structure this to be able to do this analysis?

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  • $\begingroup$ Can you give us more detail? How many observations do you have? How many for each year? $\endgroup$
    – mdewey
    Commented Oct 4, 2016 at 20:05
  • $\begingroup$ Cases per year range from several hundred to less than 10. The idea is that we are seeing a decrease in cases over years from 2008-2015 and want to see if we see still see those changes after adjusting for changes in screenings over the same years. Only the last 2 years (2014-2015) have less than 10 $\endgroup$
    – Dpatel87
    Commented Oct 5, 2016 at 1:28
  • $\begingroup$ I was not clear enough. Are you trying to fit a model with 7 observations, one for each year? $\endgroup$
    – mdewey
    Commented Oct 5, 2016 at 8:37
  • $\begingroup$ That is correct. I am using 2008 (first year) as the reference group. $\endgroup$
    – Dpatel87
    Commented Oct 5, 2016 at 14:59

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When you fit a factor (year) with 8 levels to only 8 observations you will not have any degrees of freedom left and you will have a perfect prediction. If you then try to add another predictor variable it will fail because there is nothing left to explain. What to do next depends on your underlying scientific question. You could fit year as a linear effect, you could fit year as a random effect, you could fit year using fewer levels 2008-2011 versus 2012-2015.

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