pmatrix.piecewise.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. Note that pmatrix.msm
is sufficient to calculate
transition probabilities for time-inhomogeneous models fitted using the
pci
argument to msm
.
pmatrix.piecewise.msm(
x = NULL,
t1,
t2,
times,
covariates = NULL,
ci = c("none", "normal", "bootstrap"),
cl = 0.95,
B = 1000,
cores = NULL,
qlist = NULL,
...
)
x |
A fitted multi-state model, as returned by |
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
(assuming that all elements of |
ci |
If 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 |
cores |
Number of cores to use for bootstrapping using parallel
processing. See |
qlist |
A list of transition intensity matrices, of length one greater
than the length of |
... |
Optional arguments to be passed to |
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(t_1,
t_n)
for the time interval (t_1,
t_n)
cannot be calculated from the estimated intensity matrix as
\exp((t_n - t_1) Q)
, because Q
varies within
the interval t_1, t_n
. However, if the covariates are
piecewise-constant, or can be approximated as piecewise-constant, then we
can calculate P(t_1, t_n)
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(t_1, t_n) = P(t_1, t_2) P(t_2, t_3)\ldots P(t_{n-1},
t_n)
The matrix of estimated transition probabilities P(t)
for the
time interval [t1, tn]
. That is, the probabilities of occupying
state s
at time t_n
conditionally on occupying state r
at time t_1
. Rows correspond to "from-state" and columns to
"to-state".
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
pmatrix.msm
## 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)
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