Simulate a number of individual realisations from a continuous-time Markov process. Observations of the process are made at specified arbitrary times for each individual, giving panel-observed data.
simmulti.msm(data, qmatrix, covariates=NULL, death = FALSE, start,
ematrix=NULL, misccovariates=NULL, hmodel=NULL, hcovariates=NULL,
censor.states=NULL, drop.absorb=TRUE)A data frame with columns,
Subject identification indicators
Observation times
Simulated (true) state at the corresponding time
Observed outcome at the corresponding time, if
ematrix or hmodel was supplied
Row numbers of the original data. Useful when
drop.absorb=TRUE, to show which rows were not dropped
plus any supplied covariates.
A data frame with a mandatory column named time,
representing observation times. The optional column named subject,
corresponds to subject identification numbers. If not given, all
observations are assumed to be on the same individual. Observation
times should be sorted within individuals. The optional column
named cens indicates the times at which simulated states
should be censored. If cens==0 then the state is not
censored, and if cens==k, say, then all simulated states at that
time which are in the set censor.states are replaced by
k.
Other named columns of the data frame represent any covariates,
which may be time-constant or time-dependent. Time-dependent
covariates are assumed to be constant between the observation
times.
The transition intensity matrix of the
Markov process, with any covariates set to zero. 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 )
)
List of linear covariate effects on log transition intensities. Each element is a vector of the effects of one covariate on all 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.
For example, for a multi-state model with three transition
intensities, and two covariates x and y on each
intensity,
covariates=list(x = c(-0.3,-0.3,-0.3), y=c(0.1, 0.1, 0.1))
Vector of indices of the death states. A death state is
an absorbing state whose time of entry is known exactly, but the
individual is assumed to be in an unknown transient state ("alive")
at the previous instant. This is the usual situation for times of death in
chronic disease monitoring data. For example, if you specify
death = c(4, 5) then states 4 and 5 are assumed to be death
states.
death = TRUE indicates that the
final state is a death state, and death = FALSE (the default)
indicates that there is no death state.
A vector with the same number of elements as there are distinct subjects in the data, giving the states in which each corresponding individual begins. Or a single number, if all of these are the same. Defaults to state 1 for each subject.
An optional misclassification matrix for generating observed states
conditionally on the simulated true states. As defined in
msm.
Covariate effects on misclassification
probabilities via multinomial logistic regression. Linear effects
operate on the log of each probability relative to the probability of
classification in the correct state. In same format as
covariates.
An optional hidden Markov model for generating observed
outcomes conditionally on the simulated true states. As defined in
msm.
List of the same length as hmodel, defining any covariates
governing the hidden Markov outcome models. Unlike in the
msm function, this should also define the values of the
covariate effects. Each element of the list is a named vector of the
initial values for each set of covariates for that state. For
example, for a three-state hidden Markov model with two, one and no
covariates on the state 1, 2 and 3 outcome models respectively,
hcovariates = list (c(acute=-8, age=0), c(acute=-8), NULL)
Set of simulated states which should be replaced by a censoring indicator at censoring times. By default this is all transient states (representing alive, with unknown state).
Drop repeated observations in the absorbing state, retaining only one.
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
sim.msm is called repeatedly to produce a simulated
trajectory for each individual. The state at each specified
observation time is then taken to produce a new column state.
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.
If the subject enters an absorbing state, then only the first
observation in that state is kept in the data frame. Rows corresponding to future
observations are deleted. The entry times into states given in
death are assumed to be known exactly.
sim.msm
### Simulate 100 individuals with common observation times
sim.df <- data.frame(subject = rep(1:100, rep(13,100)), time = rep(seq(0, 24, 2), 100))
qmatrix <- rbind(c(-0.11, 0.1, 0.01 ),
c(0.05, -0.15, 0.1 ),
c(0.02, 0.07, -0.09))
simmulti.msm(sim.df, qmatrix)
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