redrank  R Documentation 
This function estimates regression coefficients in reduced rank proportional hazards models for competing risks and multistate models.
redrank(
redrank,
full = ~1,
data,
R,
strata = NULL,
Gamma.start,
method = "breslow",
eps = 1e05,
print.level = 1
)
redrank 
Survival formula, starting with either Surv(time,status) ~ or with Surv(Tstart,Tstop,status) ~, followed by a formula containing covariates for which a reduced rank estimate is to be found 
full 
Optional, formula specifying that part which needs to be retained in the model (so not subject to reduced rank) 
data 
Object of class 'msdata', as prepared for instance by

R 
Numeric, indicating the rank of the solution 
strata 
Name of covariate to be used inside the

Gamma.start 
A matrix of dimension K x R, with K the number of transitions and R the rank, to be used as starting value 
method 
The method for handling ties in

eps 
Numeric value determining when the iterative algorithm is
finished (when for two subsequent iterations the difference in
loglikelihood is smaller than 
print.level 
Determines how much output is written to the screen; 0: no output, 1: iterations, for each iteration solutions of Alpha, Gamma, loglikelihood, 2: also the Cox regression results 
For details refer to Fiocco, Putter & van Houwelingen (2005, 2008).
A list with elements
Alpha 
the Alpha matrix 
Gamma 
the Gamma matrix 
Beta 
the Beta matrix corresponding to

Beta2 
the Beta matrix corresponding to

cox.itr1 
the 
alphaX 
the
matrix of prognostic scores given by 
niter 
the number of iterations needed to reach convergence 
df 
the number of regression parameters estimated 
loglik 
the loglikelihood 
Marta Fiocco and Hein Putter H.Putter@lumc.nl
Fiocco M, Putter H, van Houwelingen JC (2005). Reduced rank proportional hazards model for competing risks. Biostatistics 6, 465–478.
Fiocco M, Putter H, van Houwelingen HC (2008). Reducedrank proportional hazards regression and simulationbased prediction for multistate models. Statistics in Medicine 27, 4340–4358.
Putter H, Fiocco M, Geskus RB (2007). Tutorial in biostatistics: Competing risks and multistate models. Statistics in Medicine 26, 2389–2430.
## Not run:
# This reproduces the results in Fiocco, Putter & van Houwelingen (2005)
# Takes a while to run
data(ebmt2)
# transition matrix for competing risks
tmat < trans.comprisk(6,names=c("Relapse","GvHD","Bacterial","Viral","Fungal","Other"))
# preparing long dataset
ebmt2$stat1 < as.numeric(ebmt2$status==1)
ebmt2$stat2 < as.numeric(ebmt2$status==2)
ebmt2$stat3 < as.numeric(ebmt2$status==3)
ebmt2$stat4 < as.numeric(ebmt2$status==4)
ebmt2$stat5 < as.numeric(ebmt2$status==5)
ebmt2$stat6 < as.numeric(ebmt2$status==6)
covs < c("dissub","match","tcd","year","age")
ebmtlong < msprep(time=c(NA,rep("time",6)),
stat=c(NA,paste("stat",1:6,sep="")),
data=ebmt2,keep=covs,trans=tmat)
# The reduced rank 2 solution
rr2 < redrank(Surv(Tstart,Tstop,status) ~ dissub+match+tcd+year+age,
data=ebmtlong, R=2)
rr3$Alpha; rr3$Gamma; rr3$Beta; rr3$loglik
# The reduced rank 3 solution
rr3 < redrank(Surv(Tstart,Tstop,status) ~ dissub+match+tcd+year+age,
data=ebmtlong, R=3)
rr3$Alpha; rr3$Gamma; rr3$Beta; rr3$loglik
# The reduced rank 3 solution, with no reduction on age
rr3 < redrank(Surv(Tstart,Tstop,status) ~ dissub+match+tcd+year, full=~age,
data=ebmtlong, R=3)
rr3$Alpha; rr3$Gamma; rr3$Beta; rr3$loglik
# The full rank solution
fullrank < redrank(Surv(Tstart,Tstop,status) ~ dissub+match+tcd+year+age,
data=ebmtlong, R=6)
fullrank$Beta; fullrank$loglik
## End(Not run)
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