Well, I think you are going to need PROC NLMIXED if you want to duplicate those graphs as they fit a segmented model which is something that PROC MIXED doesn't do without some major coding. The key is to include a PREDICT statement with the out= option to get the predicted values and confidence bounds into a dataset.
However, your PROC MIXED code treats time as a categorical variable, so you can get output with breaks at each time point. Simply add outp=predicted to your model statement. This will give you a dataset named "predicted" with the estimate for each time point, as well as upper and lower (1-alpha) confidence bounds. Take that dataset as your input to PROC SGPLOT. This note https://support.sas.com/kb/42/542.html will help walk you through the plot. Note that some of the data shaping steps won't be needed as you already have the estimate and the lower and upper bounds.
SteveDenham
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