mstate (version 0.3.3)

ELOS: Expected length of stay

Description

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

Usage

ELOS(pt, tau)

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.

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

Author

Hein Putter

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)