Reduced rank proportional hazards model for competing risks and multi-state models

This function estimates regression coefficients in reduced rank proportional hazards models for competing risks and multi-state models.

redrank(
  redrank,
  full = ~1,
  data,
  R,
  strata = NULL,
  Gamma.start,
  method = "breslow",
  eps = 1e-05,
  print.level = 1
)

Arguments

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 msprep, in which to interpret the redrank and, optionally, the full formulas
R	Numeric, indicating the rank of the solution
strata	Name of covariate to be used inside the strata part of coxph
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 coxph
eps	Numeric value determining when the iterative algorithm is finished (when for two subsequent iterations the difference in log-likelihood is smaller than eps)
print.level	Determines how much output is written to the screen; 0: no output, 1: iterations, for each iteration solutions of Alpha, Gamma, log-likelihood, 2: also the Cox regression results

Value

A list with elements

Alpha

the Alpha matrix

Gamma

the Gamma matrix

Beta

the Beta matrix corresponding to covariates

Beta2

the Beta matrix corresponding to fullcovs

cox.itr1

the coxph object resulting from the last call giving Alpha

alphaX

the matrix of prognostic scores given by Alpha, n x R, with n number of subjects

niter

the number of iterations needed to reach convergence

df

the number of regression parameters estimated

loglik

the log-likelihood

Details

For details refer to Fiocco, Putter & van Houwelingen (2005, 2008).

References

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). Reduced-rank proportional hazards regression and simulation-based prediction for multi-state models. Statistics in Medicine 27, 4340--4358.

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

Author

Marta Fiocco and Hein Putter H.Putter@lumc.nl

Examples

if (FALSE) {
    # 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
}