totlos.fs  R Documentation 
The matrix whose r,s
entry is the expected amount of time spent in
state s
for a timeinhomogeneous, continuoustime Markov multistate
process that starts in state r
, up to a maximum time t
. This is
defined as the integral of the corresponding transition probability up to
that time.
totlos.fs(
x,
trans = NULL,
t = 1,
newdata = NULL,
ci = FALSE,
tvar = "trans",
sing.inf = 1e+10,
B = 1000,
cl = 0.95,
...
)
x 
A model fitted with

trans 
Matrix indicating allowed transitions. See

t 
Time or vector of times to predict up to. Must be finite. 
newdata 
A data frame specifying the values of covariates in the
fitted model, other than the transition number. See

ci 
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 
tvar 
Variable in the data representing the transition type. Not
required if 
sing.inf 
If there is a singularity in the observed hazard, for
example a Weibull distribution with 
B 
Number of simulations from the normal asymptotic distribution used to calculate variances. Decrease for greater speed at the expense of accuracy. 
cl 
Width of symmetric confidence intervals, relative to 1. 
... 
Arguments passed to 
This is computed by solving a second order extension of the Kolmogorov forward differential equation numerically, using the methods in the deSolve package. The equation is expressed as a linear system
\frac{dT(t)}{dt} = P(t)
\frac{dP(t)}{dt} = P(t) Q(t)
and solved for T(t)
and P(t)
simultaneously, where T(t)
is the matrix of total lengths of stay, 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 conditions are
T(0) = 0
and P(0) = I
.
Note that the package msm has a similar method totlos.msm
.
totlos.fs
should give the same results as totlos.msm
when
both of these conditions hold:
the timetoevent distribution is exponential for all
transitions, thus the flexsurvreg
model was fitted with
dist="exp"
, and is timehomogeneous.
the msm model was
fitted with exacttimes=TRUE
, thus all the event times are known, and
there are no timedependent covariates.
msm only allows exponential or piecewiseexponential timetoevent 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 ("clockforward") multistate
models, though no warning or error is currently given if the model is not
Markov. See totlos.simfs
for the equivalent for semiMarkov
("clockreset") models.
The matrix of lengths of stay T(t)
, if t
is of length
1, or a list of matrices if t
is longer.
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()
.
The result also has an attribute P
giving the transition probability
matrices, since these are unavoidably computed as a side effect. These are
suppressed for printing, but can be extracted with attr(...,"P")
.
Christopher Jackson chris.jackson@mrcbsu.cam.ac.uk.
totlos.simfs
, pmatrix.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))
# predict 4 years spent without BOS, 3 years with BOS, before death
# As t increases, this should converge
totlos.fs(bexp, t=10, trans=tmat)
totlos.fs(bexp, t=1000, trans=tmat)
totlos.fs(bexp, t=c(5,10), trans=tmat)
# Answers should match results in help(totlos.simfs) up to Monte Carlo
# error there / ODE solving precision here, since with an exponential
# distribution, the "semiMarkov" model there is the same as the Markov
# model here
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