Simulate one individual trajectory from a continuous-time Markov model

Simulate one realisation from a continuous-time Markov process up to a given time.

Usage

sim.msm(
  qmatrix,
  maxtime,
  covs = NULL,
  beta = NULL,
  obstimes = 0,
  start = 1,
  mintime = 0
)

Arguments

qmatrix

The transition intensity matrix of the Markov process. The diagonal of qmatrix is ignored, and computed as appropriate so that the rows sum to zero. For example, a possible qmatrix for a three state illness-death model with recovery is:

rbind( c( 0, 0.1, 0.02 ), c( 0.1, 0, 0.01 ), c( 0, 0, 0 ) )

maxtime

Maximum time for the simulated process.

covs

Matrix of time-dependent covariates, with one row for each observation time and one column for each covariate.

beta

Matrix of linear covariate effects on log transition intensities. The rows correspond to different covariates, and the columns to the transition intensities. The intensities are ordered by reading across rows of the intensity matrix, starting with the first, counting the positive off-diagonal elements of the matrix.

obstimes

Vector of times at which the covariates are observed.

start

Starting state of the process. Defaults to 1.

mintime

Starting time of the process. Defaults to 0.

Value

A list with components,

states: Simulated states through which the process moves. This ends with either an absorption before obstime, or a transient state at obstime.
times: Exact times at which the process changes to the corresponding states
qmatrix: The given transition intensity matrix

Details

The effect of time-dependent covariates on the transition intensity matrix for an individual is determined by assuming that the covariate is a step function which remains constant in between the individual's observation times.

Author

C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk

Examples



qmatrix <- rbind(
                 c(-0.2,   0.1,  0.1 ),
                 c(0.5,   -0.6,  0.1 ),
                 c(0,  0,  0)
                 )
sim.msm(qmatrix, 30)
#> $states
#> [1] 1 2 1 2 1 3
#> 
#> $times
#> [1]  0.000000  6.313054 10.649513 11.530177 11.959692 13.194049
#> 
#> $qmatrix
#>      [,1] [,2] [,3]
#> [1,] -0.2  0.1  0.1
#> [2,]  0.5 -0.6  0.1
#> [3,]  0.0  0.0  0.0
#>