quasi-complete separation in proc logistic: question about Firth method

[joesmama]

Hello,

I am running proc logistic on my dataset and have come across a quasi-complete separation error. I've managed to figure out which variable is causing the issue: a cross tabulation of two variables (dependent x independent) showed that one of the cells in the 2x2 is 0. My original logistic regression model yielded a enormous odds ratio for this variable and  CIs that are essentially +-infinity. Using Paul Allison's suggestions on dealing with the quasi-complete separation, I narrowed it down to adjusting the model to use the Firth method. Now my results look much more reasonable, although the CIs (using profile likelihood CIs) are still quite wide (n=220). My question is: Do I now report these "modified" ORs and CIs as I normally would and just mention that the Firth method was used or do I need to go into additional detail.   

Any input is appreciated. 

[Rick_SAS · Accepted solution]

I'd tell the readers just what you told us. A classical logistic regression results in a quasi-separation, so Firth’s penalized likelihood method (the FIRTH option) is used as suggested by Allison (2012). Then report likelihood-based confidence limits and likelihood ratio tests.

BTW, if your sample is small, you can also try exact logistic regression.

[joesmama]

Thank you for the response. That clarifies things.

One question: do we still report the estimates from the Firth analysis or just the confidence limits and likelihood tests?

[Rick_SAS]

Report the estimates as well.

[joesmama]

Thank you very much Rick.