Phase-type expansion of a transition intensity matrix to create a non-Markov multi-state model

Convert a multi-state model intensity matrix with one or more non-Markov states to an intensity matrix on a phase-type state space, where the non-Markov states are modelled with a phase-type approximation of a shape/scale distribution.

Usage

qphaseapprox(
  qmatrix,
  pastates,
  shape,
  scale = 1,
  family = "gamma",
  method = "moment",
  nphase = NULL,
  att = FALSE
)

Arguments

qmatrix: Intensity matrix on the observable state space. Only the rates for transitions out of Markov states are used, and values of rates for transitions out of the non-Markov state are ignored, unless there are competing next states. In that case the relative value of the intensities are interpreted as the transition probability to each next state. These transition probabilities are multiplied by the phase transition rates of the sojourn distribution in the non-Markov state to get the transition rates from the phases to the destination state.
pastates: This indicates which states (if any) are given a Weibull or Gamma sojourn distribution approximated by a phase-type model Ignored if nphase is supplied.
shape: shape parameter. This can be vectorised.
scale: scale parameter. This can be vectorised.
family: parametric family approximated by the phase-type distribution: "weibull" or "gamma"
method: (Deprecated)
nphase: Only required for models with phase-type sojourn distributions specified directly (not through pastates). nphase is a vector with one element per state, giving the number of phases per state. This element is 1 for states that do not have phase-type sojourn distributions.
att: keep attributes indicating progression and absorption states

Value

Intensity matrix on the latent state space.