pmatrix.piecewise.msm {msm} | R Documentation |
Extract the estimated transition probability matrix from a fitted
non-time-homogeneous multi-state model for a given time interval.
This is a generalisation of pmatrix.msm
to
models with time-dependent covariates.
pmatrix.piecewise.msm(x, t1, t2, times, covariates, ci=c("none","normal","bootstrap"), cl=0.95, B=1000, ...)
x |
A fitted multi-state model, as returned by
msm . This should be a non-homogeneous model, whose
transition intensity matrix depends on a time-dependent covariate. |
t1 |
The start of the time interval to estimate the transition probabilities for. |
t2 |
The end of the time interval to estimate the transition probabilities for. |
times |
Cut points at which the transition intensity matrix changes. |
covariates |
A list with number of components one greater than the length of
times . Each component of the list is specified in the same
way as the covariates argument to pmatrix.msm .
The components correspond to the covariate values in the intervals
(assuming that all elements of |
ci |
If "normal" , then calculate a confidence interval for
the transition probabilities by simulating B random vectors
from the asymptotic multivariate normal distribution implied by the
maximum likelihood estimates (and covariance matrix) of the log
transition intensities and covariate effects, then calculating the
resulting transition probability matrix for each replicate.
If
If |
cl |
Width of the symmetric confidence interval, relative to 1. |
B |
Number of bootstrap replicates, or number of normal simulations from the distribution of the MLEs |
... |
Optional arguments to be passed to MatrixExp to
control the method of computing the matrix exponential. |
Suppose a multi-state model has been fitted, in which the transition intensity matrix Q(x(t)) is modelled in terms of time-dependent covariates x(t). The transition probability matrix P(t1, tn) for the time interval (t1, tn) cannot be calculated from the estimated intensity matrix as exp((tn - t1) Q), because Q varies within the interval t1, tn. However, if the covariates are piecewise-constant, or can be approximated as piecewise-constant, then we can calculate P(t1, tn) by multiplying together individual matrices P(t_i, t_{i+1}) = exp((t_{i+1} - t_i) Q), calculated over intervals where Q is constant:
P(t1, tn) = P(t1, t2) P(t2, t3)\ldotsP(tn-1, tn)
The matrix of estimated transition probabilities P(t) for the
time interval [t1, tn]
. That is, the probabilities of
occupying state s at time tn
conditionally on occupying state r at time t1.
Rows correspond to "from-state" and columns to "to-state".
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
## Not run: ## In a clinical study, suppose patients are given a placebo in the ## first 5 weeks, then they begin treatment 1 at 5 weeks, and ## a combination of treatments 1 and 2 from 10 weeks. ## Suppose a multi-state model x has been fitted for the patients' ## progress, with treat1 and treat2 as time dependent covariates. ## Cut points for when treatment covariate changes times <- c(0, 5, 10) ## Indicators for which treatments are active in the four intervals ## defined by the three cut points covariates <- list( list (treat1=0, treat2=0), list (treat1=0, treat2=0), list(treat1=1, treat2=0), list(treat1=1, treat2=1) ) ## Calculate transition probabilities from the start of the study to 15 weeks pmatrix.piecewise.msm(x, 0, 15, times, covariates) ## End(Not run)