The methods I use fit a flexible parametric survival model that uses restricted cubic splines to model the underlying log cumulative survival function. Interactions between a covariate and followup time can be easily accommodated. Many functions can be predicted using the model estimates, including hazard, hazard differences, survival differences and hazard ratios as functions of followup time. This is all done in a suite of sas macros that implement much of what is available in Stata's user-written stpm2 module, and has been developed as a work-alike version of that module and its prediction functions. I haven't published this suite yet, but am certainly willing to share it with you
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