How to model the time of procedure (dirunal variation) in relation to outcomes?

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I have a group of patients underoging a type of procedure - I want to see if surgery in the pm is assocaited with worse outcomes (mortality, infection etc). So far, I have used a binary classification (surgery in the am amd pm) and inputed this in a logistic regression/mixed effects model.

Outcome ~ time of procedure (am/pm) + var 1 + var2 +.......

However, this realtion might be more complex/non-linear and we need another type function/model. Do you have any ideas of what model would be best suited to assess diurnal/circadian variation in outcomes ? Can we use something like a GAM model and apply smooth functinon to time ?

Thanks for your time

Daniel

Ideas on statistical design.

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