redrank function

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

Returns

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).

Examples

## 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)

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(s)

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