we are researching whether the date of a certain medical procedure impacts the complication rate of said procedure. To this end we have identified multiple risk factors we would like to study more closely (e.g. the day of the week, holiday seasons, winter/summer and so on).
Simplified, we have a table of the form
where the reference group is the subset of patients that have neither risk factor A, B or C. Please note that $A \cap B \neq \emptyset$ etc, i.e. we cannot eliminate dependency between columns.
What is now the appropriate statistical test or model to compare the individual risk groups against the reference group? Our null-hypothesis is that group A/B/C do not have more infections in comparison to the reference group.