R: Reduced rank proportional hazards model for competing risks...

redrank {mstate} | R Documentation

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

### Description

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

### Usage

    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

### Details

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

### 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

### Author(s)

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

### 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.

### 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)

[Package mstate version 0.3.2 Index]