Given a "probtrans" object, ELOS calculates the (restricted) expected
length of stay in each of the states of the multi-state model.
Value
A K x K matrix (with K number of states), with the (g,h)'th element
containing E_gh(s,tau). The starting time point s is inferred from pt
(the smallest time point, should be equal to the predt value in the
call to probtrans. The row- and column names of the matrix
have been named "from1" until "fromK" and "in1" until "inK", respectively.
Details
The object pt needs to be a "probtrans" object, obtained with
forward prediction (the default, direction="forward", in the
call to probtrans). The restriction to tau is there
because, as in ordinary survival analysis, the probability of being in a
state can be positive until infinity, resulting in infinite values. The
(restricted, until tau) expected length of stay in state h, given in state g
at time s, is given by the integral from s to tau of P_gh(s,t), see for
instance Beyersmann and Putter (2014).
Author
Hein Putter H.Putter@lumc.nl
Examples
# transition matrix for illness-death model
tmat <- trans.illdeath()
# data in wide format, for transition 1 this is dataset E1 of
# Therneau & Grambsch (2000)
tg <- data.frame(illt=c(1,1,6,6,8,9),ills=c(1,0,1,1,0,1),
dt=c(5,1,9,7,8,12),ds=c(1,1,1,1,1,1),
x1=c(1,1,1,0,0,0),x2=c(6:1))
# data in long format using msprep
tglong <- msprep(time=c(NA,"illt","dt"),status=c(NA,"ills","ds"),
data=tg,keep=c("x1","x2"),trans=tmat)
# events
events(tglong)
#> $Frequencies
#> to
#> from healthy illness death no event total entering
#> healthy 0 4 2 0 6
#> illness 0 0 4 0 4
#> death 0 0 0 6 6
#>
#> $Proportions
#> to
#> from healthy illness death no event
#> healthy 0.0000000 0.6666667 0.3333333 0.0000000
#> illness 0.0000000 0.0000000 1.0000000 0.0000000
#> death 0.0000000 0.0000000 0.0000000 1.0000000
#>
table(tglong$status,tglong$to,tglong$from)
#> , , = 1
#>
#>
#> 2 3
#> 0 2 4
#> 1 4 2
#>
#> , , = 2
#>
#>
#> 2 3
#> 0 0 0
#> 1 0 4
#>
# expanded covariates
tglong <- expand.covs(tglong,c("x1","x2"))
# Cox model with different covariate
cx <- coxph(Surv(Tstart,Tstop,status)~x1.1+x2.2+strata(trans),
data=tglong,method="breslow")
summary(cx)
#> Call:
#> coxph(formula = Surv(Tstart, Tstop, status) ~ x1.1 + x2.2 + strata(trans),
#> data = tglong, method = "breslow")
#>
#> n= 16, number of events= 10
#>
#> coef exp(coef) se(coef) z Pr(>|z|)
#> x1.1 1.4753 4.3723 1.2557 1.175 0.240
#> x2.2 0.8571 2.3563 0.8848 0.969 0.333
#>
#> exp(coef) exp(-coef) lower .95 upper .95
#> x1.1 4.372 0.2287 0.3731 51.24
#> x2.2 2.356 0.4244 0.4160 13.35
#>
#> Concordance= 0.781 (se = 0.077 )
#> Likelihood ratio test= 2.93 on 2 df, p=0.2
#> Wald test = 2.32 on 2 df, p=0.3
#> Score (logrank) test = 2.86 on 2 df, p=0.2
#>
# new data, to check whether results are the same for transition 1 as
# those in appendix E.1 of Therneau & Grambsch (2000)
newdata <- data.frame(trans=1:3,x1.1=c(0,0,0),x2.2=c(0,1,0),strata=1:3)
HvH <- msfit(cx,newdata,trans=tmat)
# probtrans
pt <- probtrans(HvH,predt=0)
# ELOS until last observed time point
ELOS(pt)
#> in1 in2 in3
#> from1 7.481061 2.180088 2.33885
#> from2 0.000000 5.000000 7.00000
#> from3 0.000000 0.000000 12.00000
# Restricted ELOS until tau=10
ELOS(pt, tau=10)
#> in1 in2 in3
#> from1 7.481061 1.228543 1.290396
#> from2 0.000000 5.000000 5.000000
#> from3 0.000000 0.000000 10.000000