# 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. ```r 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 ```r ## 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

redrank function