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)
| pt | An object of class |
|---|---|
| tau | The horizon until which ELOS is calculated; if missing, the maximum of the observed transition times is taken |
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.
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).
Hein Putter H.Putter@lumc.nl
# 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 #>#> , , = 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