I'm looking for guidance for how to plan an analysis. I am interested in temporal differences amongst two different populations. More specifically I'm interested in assessing differences in length of stay for patients admitted during the week vs weekend stratified by trauma vs urgent surgery. The hypothesis is that patients receiving urgent surgery would have a longer relative length of stay if admitted on the weekend than patients requiring trauma surgery. The data that I am using does have weekday, weekend, trauma, urgent, and length of stay, but I'm curious how to analyze this. I would appreciate any help/guidance!
Sounds like some form of regression / generalized linear model would work well. You could predict the length of stay with the weekday vs. weekend day variable, trauma vs. urgent variable, and with their interaction.
A significant interaction would suggest that intake reason has a different relation to length of stay depending on intake day, and you could then do follow-up comparisons to check whether such differences are in line with your hypothesis. If the data meets the assumptions of linear regression, you could use that. If not, some form of generalized linear model might work.