I have a question regarding how one would deal with complete separation in logistic regression when reporting the outcome for statistical analysis. For a study, we have group participants into 4 groups, depending on year of graduation, and have several dependent binomial factors we were testing for the statistical significance of the predicting power of the group of year of graduation. Out of the 4 binomial outcomes, 3 are completely fine and produce great results. The 4th, we have a cell count 0 - as one of the groups had 0 successes. My software, obviously, is not allowing me to run a logistic regression on this data, but it still looks, to the eye, statistically significant.
I would prefer to do a fourth logistic regression for consistency of the report. I need suggestions how to proceed. Some sources recommend combing groups. In our case, our groups are: [pre 2000], [2001-2005], [2006-2010], [2011-2015], and [2016+]. The [2016+] group is the one with 0 successes. Should I combine the last two groups, creating a 2011+ group? If I do this only for the last regression, does this raise questions regarding data validity. Do I explain why I did the analysis the way I did?
Any suggestions would be helpful. Thank you.