@arya had a presentation at this year’s StanCon that implemented I-splines (https://github.com/pourzanj/Stancon2018_Alzheimers). It wasn’t applied to cumulative hazards, but it means monotone splines have been successfully implemented in Stan at least once. I made a note of it then because that “natural cubic splines are close enough” argument did not seem like it was going to work in Stan for the reasons noted above. I was honestly hoping the person who first mentioned Royston and Parmar had come up with a clever way around it!
@harrelfe, by analytic form do you mean there must be a closed form for the instantaneous hazard or the cumulative hazard? I agree we absolutely need a closed form for the instantaneous hazard, but why couldn’t you evaluate the spline function at some quadrature points and use that to get the cumulative hazard? (Alternately, perhaps obtaining the cumulative hazard could be a use for the 1d integrator.)
As someone who does both time-to-event modeling and consulting with applied researchers, I don’t feel comfortable with the major Stan implementation of survival models being part of a discipline-specific R package like survHE. Time-to-event models are much more broadly applicable than just health economics— too much of the target audience is going to miss it if it’s cloaked in the language of another application area. For that reason, I’d strongly prefer either rstanarm or a standalone survival package.