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

## 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