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A model for repeated treatments and repeated outcomes

I have the following experimental design:Measurements of kidney function (in units called GFR) taken at several time points pre-operation (time points not evenly spaced) and at several time points post-operation (neither evenly spaced).
Here's an example of my data in R code:
set.seed(1)df <- data.frame(patient = letters[1:10],? ? ? ? ? ? ? ? gfr_ten_days_prop = rnorm(10,5,1), gfr_five_days_prop = rnorm(10,10,1), gfr_three_days_prop = rnorm(10,12,1),? ? ? ? ? ? ? ? gfr_one_day_postop = rnorm(10,10,1), gfr_one_day_postop = rnorm(10,5,1), gfr_one_day_postop = rnorm(10,2,1))

I'm looking for a model which will estimate the effect of pre-operation GFR on post-operation GFR, taking into account the different times at which GFRs were measured pre- and post-operation.One additional possible caveat - my data contain missing values (NAs).
I'm having a hard time seeing how a mixed-effects model fits this problem since in all the examples of repeated measures/longitudinal data I came across in each time point the response is measured whereas here it is more a predictive question - how strong does each pre-operation GFR predict pos-operation GFR, where the time at which GFRs were measured may matter.
Thanks a lot,Dan