ppass.msm {msm} | R Documentation |
Passage probabilities
Description
Probabilities of having visited each state by a particular time in a continuous time Markov model.
Usage
ppass.msm(
x = NULL,
qmatrix = NULL,
tot,
start = "all",
covariates = "mean",
piecewise.times = NULL,
piecewise.covariates = NULL,
ci = c("none", "normal", "bootstrap"),
cl = 0.95,
B = 1000,
cores = NULL,
...
)
Arguments
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 |
Details
The passage probabilities to state s
are computed by setting the
s
th 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.
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@mrc-bsu.cam.ac.uk
References
Norris, J. R. (1997) Markov Chains. Cambridge University Press.
See Also
efpt.msm
, totlos.msm
,
boot.msm
.
Examples
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)