Hello all!
I need to conduct a test for trend on percentages to get a p-value. I found the following code in a SAS community website which is similar to the data I have:
data test(keep=year case log_n);
infile datalines;
input year case n;
log_n=log(n);
output test; datalines;
2000 100 50000
2005 75 60000
2010 50 75000;
run;
proc genmod data=test;
model case=year / dist=poisson link=log offset=log_n;
run;
The output is attached.
Is it correct to say that there is a significant difference between the proportions (cases/log_n) in the 3 years based on the Pr>ChisSq
Hi Janet,
There seems to be a trend of decreasing proportions across the years; difference seems to imply that you compare two things to each other, but here there are three years to compare simultaneously.
When you select the log-link for the analysis, the data is modelled as: log(cases) = intercept + beta*year + log(offset), so the reponse variable is already in log-form. For this reason also the offset term is logged, since this is not automatically performed on right-hand side of the equation. You can check that the sample model seems to be predicting the outcome quite closely, e.g. exp(209.8649 - 0.108 * 2000 + log(50000)) is approximately 102. The small difference results from the non-linearity of the log-function.
The DF for year is one, because only one effect is estimated. If you would like to spend more degrees of freedom, you could turn year into two dummy variables and get get two coefficients comparing two of the years to a reference year. However, if you want to test a trend, then the proposed model seems to be what you are looking for.
Regards,
Timo Törmäkangas
Hi Janet,
There seems to be a trend of decreasing proportions across the years; difference seems to imply that you compare two things to each other, but here there are three years to compare simultaneously.
When you select the log-link for the analysis, the data is modelled as: log(cases) = intercept + beta*year + log(offset), so the reponse variable is already in log-form. For this reason also the offset term is logged, since this is not automatically performed on right-hand side of the equation. You can check that the sample model seems to be predicting the outcome quite closely, e.g. exp(209.8649 - 0.108 * 2000 + log(50000)) is approximately 102. The small difference results from the non-linearity of the log-function.
The DF for year is one, because only one effect is estimated. If you would like to spend more degrees of freedom, you could turn year into two dummy variables and get get two coefficients comparing two of the years to a reference year. However, if you want to test a trend, then the proposed model seems to be what you are looking for.
Regards,
Timo Törmäkangas
Hi Timo,
Thanks very much for your answer! It was very helpful. I took a few days to reply because I was gathering feedback from other sources as well.
Another opinion I found very useful was posted on a SAS community, which I'd like to share with you in case you find it useful / interesting in any way: https://communities.sas.com/t5/SAS-Statistical-Procedures/Is-it-correct-to-use-proc-genmod-when-testing-for-trends/m-p/500638#M25814
Thank you again for taking the time to reply.
Best,
Janet
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