Compute subject-specific or overall transition probabilities with standard errors

This function computes subject-specific or overall transition probabilities in multi-state models. If requested, also standard errors are calculated.

Usage

probtrans(
  object,
  predt,
  direction = c("forward", "fixedhorizon"),
  method = c("aalen", "greenwood"),
  variance = TRUE,
  covariance = FALSE
)

Arguments

object: msfit object containing estimated cumulative hazards for each of the transitions in the multi-state model and, if standard errors are requested, (co)variances of these cumulative hazards for each pair of transitions
predt: A positive number indicating the prediction time. This is either the time at which the prediction is made (if direction= "forward") or the time for which the prediction is to be made (if direction="fixedhorizon")
direction: One of "forward" (default) or "fixedhorizon", indicating whether prediction is forward or for a fixed horizon
method: A character string specifying the type of variances to be computed (so only needed if either variance or covariance is TRUE). Possible values are "aalen" or "greenwood"
variance: Logical value indicating whether standard errors are to be calculated (default is TRUE)
covariance: Logical value indicating whether covariances of transition probabilities for different states are to be calculated (default is FALSE)

Value

An object of class "probtrans", which is a list of which item [[s]] contains a data frame with the estimated transition probabilities (and standard errors if variance=TRUE) from state s. If covariance=TRUE, item varMatrix contains an array of dimension K^2 x K^2 x (nt+1) (with K the number of states and nt the distinct transition time points); the time points correspond to those in the data frames with the estimated transition probabilities. Finally, there are items trans, method, predt, direction, recording the transition matrix, and the method, predt and direction arguments used in the call to probtrans. Plot and summary methods have been defined for "probtrans" objects.

Details

For details refer to de Wreede, Fiocco & Putter (2010).

References

Andersen PK, Borgan O, Gill RD, Keiding N (1993). Statistical Models Based on Counting Processes. Springer, New York.

Putter H, Fiocco M, Geskus RB (2007). Tutorial in biostatistics: Competing risks and multi-state models. Statistics in Medicine 26, 2389–2430.

Therneau TM, Grambsch PM (2000). Modeling Survival Data: Extending the Cox Model. Springer, New York.

de Wreede LC, Fiocco M, and Putter H (2010). The mstate package for estimation and prediction in non- and semi-parametric multi-state and competing risks models. Computer Methods and Programs in Biomedicine 99, 261–274.

de Wreede LC, Fiocco M, and Putter H (2011). mstate: An R Package for the Analysis of Competing Risks and Multi-State Models. Journal of Statistical Software, Volume 38, Issue 7.

Author

Liesbeth de Wreede and 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)
# predictions from state 1
pt[[1]]
#>   time   pstate1    pstate2     pstate3        se1        se2        se3
#> 1    0 1.0000000 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000
#> 2    1 0.9299816 0.06204689 0.007971491 0.08750408 0.08250577 0.02915069
#> 3    5 0.9299816 0.00000000 0.070018378 0.08750408 0.00000000 0.08750408
#> 4    6 0.6776902 0.25229141 0.070018378 0.22689332 0.21903899 0.08750408
#> 5    7 0.6776902 0.12614570 0.196164083 0.22689332 0.12638316 0.14680748
#> 6    8 0.4757726 0.12614570 0.398081646 0.23614089 0.12638316 0.19877253
#> 7    9 0.0000000 0.47577265 0.524227350 0.00000000 0.53115171 0.53115171
#> 8   12 0.0000000 0.00000000 1.000000000 0.00000000 0.00000000 0.00000000