ELOS function

Expected length of stay

Given a "probtrans" object, ELOS calculates the (restricted) expected length of stay in each of the states of the multi-state model.

ELOS(pt, tau)

Arguments

• pt: An object of class "probtrans"
• tau: The horizon until which ELOS is calculated; if missing, the maximum of the observed transition times is taken

Returns

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).

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)
table(tglong$status,tglong$to,tglong$from)
# 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)
# 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)
# Restricted ELOS until tau=10
ELOS(pt, tau=10)

Author(s)

Hein Putter H.Putter@lumc.nl