One thing that jumps out at me about the summing to get an exposure variable in a longitudinal study is that the shape of the exposure likely will have a profound effect on the response - suppose all the mass for exposure is at time=0 and no other exposure compared to equal exposure at the various time points such that the sum is identical in both cases. That would almost certainly lead to different responses over time.
I don't know if this would work or not, but you might consider a multimember EFFECT, where the inputs in the EFFECT statement are the current exposure level and lagged values of the exposure level. Run something that calculates the autoregression to get the number of lags you might need, stopping when the autocorrelation levels out (a sill in a semivariogram). If there are a lot of time points, you might need to thin them for inputs. I would start with patients that completed the trial, and then work on developing methods to deal with missing measurements, either at random or due to drop out.
SteveDenham
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