# Modelling transition times parametrically in multi-state models (in R)

I've been trying to understand multi-state modelling (MSM) for my use case, which is a simple illness-death model. For a standard 2-state survival analysis I often use parametric models of the time-to-event, as it is easier to extrapolate my model to predict pathways for new individuals. I'm a fan of the flexsurv R package for this purpose.

However, the bulk of the R packages for MSM seem to involve non or semi-parametric methods, such as mstate which uses the standard Cox formulation for modelling the transition hazards. Another popular package, msm, uses Hidden Markov Models.

I'm curious as to why modelling the transition times with standard parametric families such as the Weibull isn't commonly used (as far as I can tell).

For example, in my illness death model I could fit three separate Weibull models to the three different transitions, rather than using the coxph function from the survival package as described by Putter http://onlinelibrary.wiley.com/doi/10.1002/sim.2712/full

Would modelling these transitions parametrically be correct, or am I breaking any fundamental assumption? If so, how would I then obtain the transition probabilities

$P_{ij}(s, t) = Pr(X(t) = i | X(s) = j)$

From what I've read, the common way of obtaining these is using the non-parametric Aalen-Johansen estimator from the baseline hazards of a Cox model of the transition hazards.

• I hoped you had an extensive reply here.. – Marcin Kosiński Jan 23 '18 at 14:32