Passage probabilities
Description
Probabilities of having visited each state by a particular time in a continuous time Markov model.
Usage
1 2 3 4 
Arguments
x 
A fitted multistate 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 timeinhomogeneous models. 
piecewise.covariates 
Currently ignored: not implemented for timeinhomogeneous 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 
Details
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 timehomogeneous Markov models. For timeinhomogeneous models the covariates are held constant at the value supplied, by default the column means of the design matrix over all observations.
Value
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.
Author(s)
C. H. Jackson chris.jackson@mrcbsu.cam.ac.uk
References
Norris, J. R. (1997) Markov Chains. Cambridge University Press.
See Also
efpt.msm
, totlos.msm
, boot.msm
.
Examples
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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