Simulate multiple trajectories from a multi-state Markov model with arbitrary observation times
Source:R/simul.R
simmulti.msm.RdSimulate 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.
Usage
simmulti.msm(
data,
qmatrix,
covariates = NULL,
death = FALSE,
start,
ematrix = NULL,
misccovariates = NULL,
hmodel = NULL,
hcovariates = NULL,
censor.states = NULL,
drop.absorb = TRUE
)Arguments
- data
A data frame with a mandatory column named
time, representing observation times. The optional column namedsubject, 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 namedcensindicates the times at which simulated states should be censored. Ifcens==0then the state is not censored, and ifcens==k, say, then all simulated states at that time which are in the setcensor.statesare replaced byk. 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.- qmatrix
The transition intensity matrix of the Markov process, with any covariates set to zero. The diagonal of
qmatrixis ignored, and computed as appropriate so that the rows sum to zero. For example, a possibleqmatrixfor 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 ) )- covariates
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
xandyon each intensity,covariates=list(x = c(-0.3,-0.3,-0.3), y=c(0.1, 0.1, 0.1))- death
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 = TRUEindicates that the final state is a death state, anddeath = FALSE(the default) indicates that there is no death state.- start
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.
- ematrix
An optional misclassification matrix for generating observed states conditionally on the simulated true states. As defined in
msm.- misccovariates
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.- hmodel
An optional hidden Markov model for generating observed outcomes conditionally on the simulated true states. As defined in
msm. Multivariate outcomes (hmmMV) are not supported.- hcovariates
List of the same length as
hmodel, defining any covariates governing the hidden Markov outcome models. Unlike in themsmfunction, 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)- censor.states
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.absorb
Drop repeated observations in the absorbing state, retaining only one.
Value
A data frame with columns,
- subject
Subject identification indicators
- time
Observation times
- state
Simulated (true) state at the corresponding time
- obs
Observed outcome at the corresponding time, if
ematrixorhmodelwas supplied- keep
Row numbers of the original data. Useful when
drop.absorb=TRUE, to show which rows were not dropped
plus any supplied covariates.
Details
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.
Author
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
Examples
### 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)
#> subject time state keep
#> 1 1 0 1 1
#> 2 1 2 3 2
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#> 726 56 20 1 726
#> 727 56 22 1 727
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