Description Usage Arguments Details Value Author(s) References See Also Examples
Probabilities of having visited each state by a particular time in a continuous time Markov model.
1 2 3 4 |
x |
A fitted multi-state model, as returned by
|
qmatrix |
Instead of |
tot |
Finite time to forecast the passage probabilites for. |
start |
Starting state (integer). By default ( Alternatively, this can be used to obtain passage probabilities
from a set of states, rather than single states. To
achieve this, |
covariates |
Covariate values defining the intensity matrix for
the fitted model |
piecewise.times |
Currently ignored: not implemented for time-inhomogeneous models. |
piecewise.covariates |
Currently ignored: not implemented for time-inhomogeneous models. |
ci |
If If If |
cl |
Width of the symmetric confidence interval, relative to 1. |
B |
Number of bootstrap replicates. |
cores |
Number of cores to use for bootstrapping using parallel
processing. See |
... |
Arguments to pass to |
The passage probabilities to state s are computed by
setting the sth row of the transition intensity matrix Q
to zero, giving an intensity matrix Q* for a simplified model structure
where state s is absorbing. The probabilities of passage are
then equivalent to row s of the transition probability matrix
Exp(tQ*) under this simplified model for t=tot
.
Note this is different from the probability of occupying each state at
exactly time t, given by pmatrix.msm
. The passage
probability allows for the possibility of having visited the state
before t, but then occupying a different state at t.
The mean of the passage distribution is the expected first passage
time, efpt.msm
.
This function currently only handles time-homogeneous Markov models. For time-inhomogeneous models the covariates are held constant at the value supplied, by default the column means of the design matrix over all observations.
A matrix whose r, s entry is the probability of having visited state s at least once before time t, given the state at time 0 is r. The diagonal entries should all be 1.
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
Norris, J. R. (1997) Markov Chains. Cambridge University Press.
efpt.msm
, totlos.msm
, boot.msm
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | Q <- rbind(c(-0.5, 0.25, 0, 0.25), c(0.166, -0.498, 0.166, 0.166),
c(0, 0.25, -0.5, 0.25), c(0, 0, 0, 0))
## ppass[1,2](t) converges to 0.5 with t, since given in state 1, the
## probability of going to the absorbing state 4 before visiting state
## 2 is 0.5, and the chance of still being in state 1 at t decreases.
ppass.msm(qmatrix=Q, tot=2)
ppass.msm(qmatrix=Q, tot=20)
ppass.msm(qmatrix=Q, tot=100)
Q <- Q[1:3,1:3]; diag(Q) <- 0; diag(Q) <- -rowSums(Q)
## Probability of about 1/2 of visiting state 3 by time 10.5, the
## median first passage time
ppass.msm(qmatrix=Q, tot=10.5)
## Mean first passage time from state 2 to state 3 is 10.02: similar
## to the median
efpt.msm(qmatrix=Q, tostate=3)
|
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