The transition probability matrix for time-inhomogeneous Markov multi-state
models fitted to time-to-event data with flexsurvreg. This
has \(r,s\) entry giving the probability that an individual is in state
\(s\) at time \(t\), given they are in state \(r\) at time \(0\).
pmatrix.fs(
x,
trans = NULL,
t = 1,
newdata = NULL,
condstates = NULL,
ci = FALSE,
tvar = "trans",
sing.inf = 1e+10,
B = 1000,
cl = 0.95,
tidy = FALSE,
...
)The transition probability matrix, if t is of length 1. If t is longer, return a list of matrices, or a data frame if tidy is TRUE.
If ci=TRUE, each element has attributes "lower" and
"upper" giving matrices of the corresponding confidence limits.
These are formatted for printing but may be extracted using attr().
A model fitted with flexsurvreg. See
msfit.flexsurvreg for the required form of the model and the
data. Additionally, this must be a Markov / clock-forward model, but can
be time-inhomogeneous. See the package vignette for further explanation.
x can also be a list of models, with one component for each
permitted transition, as illustrated in msfit.flexsurvreg.
Matrix indicating allowed transitions. See
msfit.flexsurvreg.
Time or vector of times to predict state occupancy probabilities for.
A data frame specifying the values of covariates in the
fitted model, other than the transition number. See
msfit.flexsurvreg.
xInstead of the unconditional probability of being in state \(s\) at time \(t\) given state \(r\) at time 0, return the probability conditional on being in a particular subset of states at time \(t\). This subset is specified in the condstates argument, as a vector of character labels or integers.
This is used, for example, in competing risks situations, e.g. if the competing states are death or recovery from a disease, and we want to compute the probability a patient has died, given they have died or recovered. If these are absorbing states, then as \(t\) increases, this converges to the case fatality ratio. To compute this, set \(t\) to a very large number, Inf will not work.
Return a confidence interval calculated by simulating from the
asymptotic normal distribution of the maximum likelihood estimates. Turned
off by default, since this is computationally intensive. If turned on,
users should increase B until the results reach the desired
precision.
Variable in the data representing the transition type. Not
required if x is a list of models.
If there is a singularity in the observed hazard, for
example a Weibull distribution with shape < 1 has infinite hazard at
t=0, then as a workaround, the hazard is assumed to be a large
finite number, sing.inf, at this time. The results should not be
sensitive to the exact value assumed, but users should make sure by
adjusting this parameter in these cases.
Number of simulations from the normal asymptotic distribution used to calculate variances. Decrease for greater speed at the expense of accuracy.
Width of symmetric confidence intervals, relative to 1.
If TRUE then return the results as a tidy data frame
Arguments passed to ode in deSolve.
Christopher Jackson chris.jackson@mrc-bsu.cam.ac.uk.
This is computed by solving the Kolmogorov forward differential equation numerically, using the methods in the deSolve package. The equation is
$$\frac{dP(t)}{dt} = P(t) Q(t)$$
where \(P(t)\) is the transition probability matrix for time \(t\), and \(Q(t)\) is the transition hazard or intensity as a function of \(t\). The initial condition is \(P(0) = I\).
Note that the package msm has a similar method pmatrix.msm.
pmatrix.fs should give the same results as pmatrix.msm when
both of these conditions hold:
the time-to-event distribution is exponential for all
transitions, thus the flexsurvreg model was fitted with
dist="exp" and the model is time-homogeneous.
the msm
model was fitted with exacttimes=TRUE, thus all the event times are
known, and there are no time-dependent covariates.
msm only allows exponential or piecewise-exponential time-to-event distributions, while flexsurvreg allows more flexible models. msm however was designed in particular for panel data, where the process is observed only at arbitrary times, thus the times of transition are unknown, which makes flexible models difficult.
This function is only valid for Markov ("clock-forward") multi-state
models, though no warning or error is currently given if the model is not
Markov. See pmatrix.simfs for the equivalent for semi-Markov
("clock-reset") models.
pmatrix.simfs, totlos.fs,
msfit.flexsurvreg.
# BOS example in vignette, and in msfit.flexsurvreg
bexp <- flexsurvreg(Surv(Tstart, Tstop, status) ~ trans,
data=bosms3, dist="exp")
tmat <- rbind(c(NA,1,2),c(NA,NA,3),c(NA,NA,NA))
# more likely to be dead (state 3) as time moves on, or if start with
# BOS (state 2)
pmatrix.fs(bexp, t=c(5,10), trans=tmat)
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