R: Computes the Survival Curve in a Bayesian analysis for a...

predict.DPsurvint {DPpackage} | R Documentation

## 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

    ## S3 method for class 'DPsurvint'
    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.

### 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) ~ Beta(a^{(j)}(t),b^{(j)}(t))

where,

a^{(j)}(t)=α^{(j)} G_0^{(j)}( (t \exp(X β^{(j)}) , ∞) ) + ∑_{i=1}^n δ_{V^{(j)}_i} ( (t \exp(X β^{(j)}) , ∞) )

and

b^{(j)}(t)=α^{(j)}+N - a^{(j)}(t)

### 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`.

### Author(s)

Alejandro Jara <atjara@uc.cl>

### 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)

[Package DPpackage version 1.1-7.4 Index]