spBayesSurv (version 1.1.1)

indeptCoxph: Bayesian Proportional Hazards Model

Description

This function fits a Bayesian proportional hazards model for non-spatial right censored time-to-event data.

Usage

indeptCoxph(formula, data, na.action, prediction=NULL, 
            mcmc=list(nburn=3000, nsave=2000, nskip=0, ndisplay=500), 
            prior=NULL, state=NULL, scale.designX=TRUE)

Arguments

formula

a formula expression with the response returned by the Surv function in the survival package. It currently only supports right-censoring.

data

a data frame in which to interpret the variables named in the formula argument.

na.action

a missing-data filter function, applied to the model.frame.

prediction

a list giving the information used to obtain conditional inferences. The list includes the following element: xpred giving the npred by p covariates matrix, used for prediction. If prediction=NULL, xpred will be set to be the design matrix used in formula.

mcmc

a list giving the MCMC parameters. The list must include the following elements: nburn an integer giving the number of burn-in scans, nskip an integer giving the thinning interval, nsave an integer giving the total number of scans to be saved, ndisplay an integer giving the number of saved scans to be displayed on screen (the function reports on the screen when every ndisplay iterations have been carried out).

prior

a list giving the prior information. The list includes the following elements: M an integer giving the total number of cut points for baseline hazard. See Zhou, Hanson and Zhang (2017) for more detailed hyperprior specifications.

state

a list giving the current value of the parameters. This list is used if the current analysis is the continuation of a previous analysis.

scale.designX

flag to indicate wheter the design matrix X will be centered by column means and scaled by column standard deviations, where TRUE indicates yes. The default is TRUE for improving numerical stability. Even when it is scaled, the reported regression coefficients are in original scales. Note if we want to specify informative priors for regression coefficients, these priors should correspond to scaled predictors when scale.designX=TRUE.

Value

The results include the MCMC chains for the parameters discussed in Zhou, Hanson and Zhang (2017). Use names to find out what they are.

Details

This function fits a Bayesian proportional hazards model (Zhou, Hanson and Zhang, 2017) for non-spatial right censored time-to-event data.

References

Zhou, H., Hanson, T., and Knapp, R. (2015). Marginal Bayesian nonparametric model for time to disease arrival of threatened amphibian populations. Biometrics, 71(4): 1101-1110.

See Also

spCopulaCoxph, GetCurves

Examples

# NOT RUN {
###############################################################
# A simulated data: Cox PH
###############################################################
rm(list=ls())
library(survival)
library(spBayesSurv)
library(coda)
## True parameters 
betaT = c(1,1); 
n=100; 
## Baseline Survival
f0oft = function(t) 0.5*dlnorm(t, -1, 0.5)+0.5*dlnorm(t,1,0.5);
S0oft = function(t) (0.5*plnorm(t, -1, 0.5, lower.tail=FALSE)+
                       0.5*plnorm(t, 1, 0.5, lower.tail=FALSE))
## The Survival function:
Sioft = function(t,x)  exp( log(S0oft(t))*exp(sum(x*betaT)) ) ;
fioft = function(t,x) exp(sum(x*betaT))*f0oft(t)/S0oft(t)*Sioft(t,x);
Fioft = function(t,x) 1-Sioft(t,x);
## The inverse for Fioft
Finv = function(u, x) uniroot(function (t) Fioft(t,x)-u, lower=1e-100, 
                              upper=1e100, extendInt ="yes", tol=1e-6)$root

## generate x 
x1 = rbinom(n, 1, 0.5); x2 = rnorm(n, 0, 1); X = cbind(x1, x2);
## generate survival times
u = runif(n);
tT = rep(0, n);
for (i in 1:n){
  tT[i] = Finv(u[i], X[i,]);
}

### ----------- right-censored -------------###
t_obs=tT 
Centime = runif(n, 2, 6);
delta = (tT<=Centime) +0 ; 
length(which(delta==0))/n; # censoring rate
rcen = which(delta==0);
t_obs[rcen] = Centime[rcen]; ## observed time 
## make a data frame
d = data.frame(tobs=t_obs, x1=x1, x2=x2, delta=delta, tT=tT); 
table(d$delta)/n;

###############################################################
# Independent Cox PH
###############################################################
# MCMC parameters
nburn=500; nsave=300; nskip=0;
# Note larger nburn, nsave and nskip should be used in practice.
mcmc=list(nburn=nburn, nsave=nsave, nskip=nskip, ndisplay=1000);
prior = list(M=10, r0=1);
# Fit the Cox PH model
res1 = indeptCoxph(formula = Surv(tobs, delta)~x1+x2, data=d, 
                   prior=prior, mcmc=mcmc);
sfit1=summary(res1); sfit1;
## traceplot
par(mfrow = c(2,2))
traceplot(mcmc(res1$beta[1,]), main="beta1")
traceplot(mcmc(res1$beta[2,]), main="beta2")
traceplot(mcmc(res1$h.scaled[2,]), main="h")
traceplot(mcmc(res1$h.scaled[3,]), main="h")

############################################
## Curves
############################################
wide=0.1;
tgrid = seq(1e-10,4,wide);
ngrid = length(tgrid);
p = length(betaT); # number of covariates
xpred = rbind(c(0,0), c(0,1)); 
estimates=plot(res1, xpred=xpred, tgrid=tgrid);
Shat = estimates$Shat;

## plot
par(mfrow = c(1,1))
plot(tgrid, Sioft(tgrid, xpred[2,]), "l", lwd=3);
lines(tgrid, Sioft(tgrid, xpred[1,]), "l", lwd=3);
lines(estimates$tgrid, estimates$Shat[,1], lty=2, lwd=3)
lines(estimates$tgrid, estimates$Shatlow[,1], lty=3, lwd=1)
lines(estimates$tgrid, estimates$Shatup[,1], lty=3, lwd=1)
lines(estimates$tgrid, estimates$Shat[,2], lty=2, lwd=3)
lines(estimates$tgrid, estimates$Shatlow[,2], lty=3, lwd=1)
lines(estimates$tgrid, estimates$Shatup[,2], lty=3, lwd=1)
# }