timereg (version 1.7.0)

additive.pls: Fits PLS for additive hazards model

Description

Fits the partial least squares estimator for the additive risk model. Time dependent variables and counting process data (multiple events per subject) are possible.

The modelling formula uses the standard survival modelling given in the survival package.

Covariates $Z_1,...,Z_p$, fixed covariates $F(t)$. Algorithm : 1) For pls components $X_1,...,X_K$, fits $$\lambda_0(t) + \alpha^T(t) F(t) + \sum_{j=1}^K X_j(t) \gamma_j(t) + Z_i(t) \beta_i^{K+1}$$ for $i=1,...,p$ 2) compute new pls components $X_{K+1} = \sum \beta_i^{K+1} Z_i(t)$ and iterate.

Usage

additive.pls(formula = formula(data), data = sys.parent(), 
start.time=0,max.time=NULL,id=NULL, pls.dim=1, 
silent=1)

Arguments

formula

a formula object with the response on the left of a '~' operator, and the independent terms on the right as regressors. The response must be a survival object as returned by the `Surv' function.

The const terms are kept as fixed covariates that are no

data

a data.frame with the variables.

start.time

start of observation period where estimates are computed.

max.time

end of observation period where estimates are computed. Estimates thus computed from [start.time, max.time]. Default is max of data.

id

For timevarying covariates the variable must associate each record with the id of a subject.

pls.dim

number of pls components

silent

set to 1 to avoid printing of warnings for non-inverible design-matrices for different timepoints, default is 0.

Value

• returns an object with the following arguments:
• baseline
  baseline of the semparametric additive risk model
• pls.comp
  the pls components, i.e. the covariates multipled on the beta coefficients.
• beta
  risk regression coefficients related to the pls components.
• beta.pls
  regression coefficients that defines the pls componets.
• tbeta.pls
  the combined regression coefficients from the pls components and the regression coefficients, these leads to risk predictions when applied to new covariates.

Details

const() specifies the $F(t)$ covariates in the above model.

References

Martinussen and Scheike, Dynamic Regression Models for Survival Data, Springer (2006).

Martinussen and Scheike, The Aalen additive hazards model with high-dimensional regressors, (2009), Lifetime Data Anal.

Examples

data(mypbc)
pbc<-mypbc
pbc$time<-pbc$time+runif(418)*0.1; pbc$time<-pbc$time/365
pbc<-subset(pbc,complete.cases(pbc));
covs<-as.matrix(pbc[,-c(1:3,6)])
covs<-cbind(covs[,c(1:6,16)],log(covs[,7:15]))
covs<-scale(covs);

### 5 PLS components for the 16 covariates 
### based on Gui-Li approach with constant effects
out<-additive.pls(Surv(time,status>=1)~covs,pbc,max.time=7,pls.dim=5)

### survival predictions
par(mfrow=c(1,3))
pout=predict.pls(out,Z=covs)
matplot(pout$times,t(pout$surv[1:20,]),type="l",ylim=c(0,1),xlab="time",ylab="survival")

### cross-validated number of pls components

outcv<-pls.surv.cv(Surv(time,status>=1)~covs,pbc,max.time=7,pls.dims=0:2)
plot(outcv$pls.dims,outcv$cv,type="l")

out2<-additive.pls(Surv(time,status>=1)~covs,pbc,max.time=7,
pls.dim=outcv$cv.dim)

pout=predict.pls(out2, Z= covs)
matplot(pout$times,t(pout$surv[1:20,]),type="l",ylim=c(0,1),
xlab="time",ylab="survival")

### 2 PLS components for the 3 covariates 
### age and sex are fixed covariates 
data(sTRACE)
out<-additive.pls(Surv(time,status==9)~const(age)+const(sex)+
vf+diabetes+chf,sTRACE,max.time=7,pls.dim=2,silent=1)