DPpackage (version 1.1-6)

predict.DPsurvint: Computes the Survival Curve in a Bayesian analysis for a semiparametric AFT regression model

Description

This function generates a posterior density sample of the Survival curve from a semiparametric AFT regression model for interval-censored data.

Usage

"predict"(object,grid,xnew=NULL,hpd=TRUE, ...)

Arguments

object

DPsurvint fitted model object.

grid

a vector of grid points where the survival curve should be evaluated.

xnew

an optional matrix containing the value of the covariables with which to predict. If omitted, the baseline survival information is calculated.

hpd

a logical variable indicating whether a 95HPD interval is calculated, TRUE, or a 95Credibility interval is caculated, FALSE, for the survival curve at each grid point. The default value is TRUE.

...

further arguments to be passed.

Value

An object of class predict.DPsurvint representing the survival information arising from a DPsurvint model fit. The results include the posterior mean (pmean), the posterior median (pmedian), the posterior standard deviation (psd), the naive standard error (pstd) and the limits of the HPD or credibility intervals, plinf and plsup.

Details

This function computes the survival curve based on the fit of a Mixture of Dirichlet process in a AFT regression model for interval censored data (Hanson and Johnson, 2004). Given a MCMC sample of size $J$ of the parameters, a sample of the predictive survival curve for $X$ is drawn as follows: for the MCMC scan $j$ of the posterior distribution, with $j=1,...,J$, we sample from:

$$ S^{(j)}(t|X,data) \sim Beta(a^{(j)}(t),b^{(j)}(t))$$ where,

$$a^{(j)}(t)=\alpha^{(j)} G_0^{(j)}( (t \exp(X \beta^{(j)}) , \infty) ) + \sum_{i=1}^n \delta_{V^{(j)}_i} ( (t \exp(X \beta^{(j)}) , \infty) )$$ and $$b^{(j)}(t)=\alpha^{(j)}+N - a^{(j)}(t)$$

References

Doss, H. (1994). Bayesian nonparametric estimation for incomplete data using mixtures of Dirichlet priors. The Annals of Statistics, 22: 1763 - 1786.

Hanson, T., and Johnson, W. (2004) A Bayesian Semiparametric AFT Model for Interval-Censored Data. Journal of Computational and Graphical Statistics, 13: 341-361.

See Also

DPsurvint

Examples

## Not run: 
#     ####################################
#     # A simulated Data Set
#     ####################################
# 
#      ind<-rbinom(100,1,0.5)
#      vsim<-ind*rnorm(100,1,0.25)+(1-ind)*rnorm(100,3,0.25)
# 
#      x1<-rep(c(0,1),50)
#      x2<-rnorm(100,0,1)
# 
#      etasim<-x1+-1*x2
#      time<-vsim*exp(-etasim)
# 
#      y<-matrix(-999,nrow=100,ncol=2)
# 
#      for(i in 1:100){
#         for(j in 1:15){
#          if((j-1)<time[i] & time[i]<=j){
#             y[i,1]<-j-1
#             y[i,2]<-j
#          }
#      }
#      if(time[i]>15)y[i,1]<-15
#      }
# 
#     # Initial state
#       state <- NULL
# 
#     # MCMC parameters
# 
#       nburn<-5000
#       nsave<-10000
#       nskip<-10
#       ndisplay<-50
#       mcmc <- list(nburn=nburn,nsave=nsave,nskip=nskip,
#                    ndisplay=ndisplay,tune=0.125)
# 
#     # Prior information
#       prior <- list(alpha=10,beta0=rep(0,2),Sbeta0=diag(100000,2),
#                     m0=0,s0=1,tau1=0.01,tau2=0.01)
# 
# 
#     # Fit the model
# 
#       fit1 <- DPsurvint(y~x1+x2,prior=prior,mcmc=mcmc,
#                         state=state,status=TRUE) 
#       fit1
# 
#     # Summary with HPD and Credibility intervals
#       summary(fit1)
#       summary(fit1,hpd=FALSE)
# 
# 
#     # Plot model parameters
#       plot(fit1)
#       plot(fit1,nfigr=2,nfigc=2)	
# 
#     # Plot an specific model parameter
#       plot(fit1,ask=FALSE,nfigr=1,nfigc=2,param="x1")	
#       plot(fit1,ask=FALSE,nfigr=1,nfigc=2,param="mu")	
# 
# 
#     # Predictive information for baseline survival
#       grid<-seq(0.00001,14,0.5)
#       pred<-predict(fit1,grid=grid)
#       
#     # Plot Baseline information with and without Credibility band
#       plot(pred)
#       plot(pred,band=TRUE)
#   
#     # Predictive information with covariates
#       npred<-10
#       xnew<-cbind(rep(1,npred),seq(-1.5,1.5,length=npred))
#       xnew<-rbind(xnew,cbind(rep(0,npred),seq(-1.5,1.5,length=npred)))
#       grid<-seq(0.00001,14,0.5)
#       pred<-predict(fit1,xnew=xnew,grid=grid)
# 
#     # Plot Baseline information
#       plot(pred,band=TRUE)
# ## End(Not run)