TransModel (version 1.0)

TransModel: Fit linear transformation models for censored data

Description

This function is used to fit a linear transformation model, such as the proportional hazards model or proportional odds model, to the right censored survival data.

Usage

TransModel(formula = formula(data), data = parent.frame(),r,CICB.st,dx,iter.max,num.sim)

Arguments

formula

A survival formula based on Surv function, containg survival time, right censoring indicator and coavariates.

data

Data set with all the variables needed in formula.

r

Parameter in the hazard function, used to define different linear models. See details for more information.

CICB.st

Whether or not the perturbation for the 95% confidence interval and confidence bands will be done. The default value is FALSE.

dx

Upbound of convergence limit. Default is 0.001.

iter.max

Maximum number of iterations before convergence. Default is 100.

num.sim

The number of perturbation, only works when CICB.st=TRUE. Default is 200.

Value

coefficients

Estimated coefficients for covariates in the specified linear transformation model.

vcov

Estimated covariance matix for the coefficients.

ord.time

Sorted survival time of original dataset.

St

Baseline survival probabilities with regard to ord.time.

converged

Convergence status, 0 indicates converged, and number of iterations used for convergence.

Details

In the linear transformation model H(t)=-b'z+e, the hazard function for error term e is defined as: h(x)=exp(x)/(1+r*exp(x)), where the parameter r can be changed for different models. For example, r=0 refers to the proportional hazards model and r=1 refers to a proportional odds model. The default value for r is 0.

References

Kani Chen, et al., Semiparametric analysis of transformation models with censored data. Biometrika, 89(3), 659-668, 2002.

Examples

beta0 = c(1,-1)
# Fit proportional hazards model
data(PH_examp)
mod1<-TransModel(formula=Surv(time,status)~gender+age,data=PH_examp,r=0)
print(mod1)
summary(mod1)
mod1$coefficients
mod1$vcov
mod1$converged

# Estimated baseline survival function
pred1<-predict(mod1,covar=data.frame(gender=0,age=0))
plot(pred1)
lines(pred1$time,exp(-((exp(2*pred1$time)-1)/2)),col=3) # True value

### Not Run ###
# survival estimate with 95% pointwise CI and overall CB
# mod1<-TransModel(formula=Surv(time,status)~gender+age,data=PH_examp,r=0,CICB.st=TRUE,num.sim=50)
# pred1<-predict(mod1,covar=data.frame(gender=0,age=0))
# plot(pred1,lty=1,col=1,CI=TRUE,CB=TRUE)
# lines(pred1$time,exp(-((exp(2*pred1$time)-1)/2)),col=3) # True value

# compare survival curve for gender=0 or 1, age=0
# pred2<-predict(mod1,covar=data.frame(gender=1,age=0))
# plot(pred1,lty=2,col=1)
# lines(pred2$time,pred2$survival,type="s",lty=2,col=2)
# lines(pred1$time,exp(-((exp(2*pred1$time)-1)/2)),col=1) # True value
# lines(pred2$time,exp(-((exp(2*pred2$time)-1)/2))^exp(sum(beta0*c(1,0))),col=2) # True value

# Fit proportional odds model
data(PO_examp)
mod2=TransModel(Surv(time,status)~gender+age,data=PO_examp,r=1)
print(mod2)
summary(mod2)
pred2<-predict(mod2,covar=data.frame(gender=0,age=0))