I am going to analyse data with multiple recurring events and additional terminal event. The recurrent events are of the same kind, no hierarchy in them (like in the Prentice-Williams-Petersen). The terminal event, the "elimination from experiment" is single and precludes all over events, it is an absorbing state.
I found two methods of survival analysis able to handle it: joint frailty models and multi-state model. The first is parametric, the second seems a non-parametric one. I am trying to figure out which one may be better and when.
It's like Cox and AFT. The first is semi-parametric, doesn't have any distributional assumptions, and deals with proportional hazards, while the second is parametric, doesn't care of the proportionality in hazards and deals with time-to-event. They answer different questions, however, under special conditions (Weibull distribution), the two can return the same results differently expressed (scaled), so PH agrees with the TTE.
My question about frailty and multi-state models is of this nature - do they answer different questions? Can they be comparable under certain conditions? If they do the same - which one seems to be better and when?
If you had to choose, which one would you use and why in general? Let us assume both methods are available in your favourite statistical tool.
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Rondeau, V., Marzroui, Y., & Gonzalez, J. (2012). frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation. Journal of Statistical Software, 47(4), 1 - 28. doi:http://dx.doi.org/10.18637/jss.v047.i04
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