SuperSurvRegBayes: Bayesian Semiparametric Super Survival Model

Description

This function fits a super survival model. It can fit both Case I and Case II interval censored data, as well as standard right-censored, uncensored, and mixtures of these. The Bernstein Polynomial Prior is used for fitting the baseline survival function.

Usage

SuperSurvRegBayes(formula, data, na.action, dist="lognormal",  mcmc=list(nburn=3000, nsave=2000, nskip=0, ndisplay=500), prior=NULL, state=NULL, truncation_time=NULL, subject.num=NULL,  InitParamMCMC=FALSE, scale.designX=TRUE)

Arguments

formula

a formula expression with the response returned by the Surv function in the survival package. It supports right-censoring, left-censoring, interval-censoring, and mixtures of them.

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.

dist

centering distribution for MPT. Choices include "loglogistic", "lognormal", and "weibull".

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: maxL an integer giving the maximum level of MPT, a0 and b0 gamma prior of the precision parameter of MPT, Shat the initial covariance matrix of adaptive M-H for each of the beta_h, beta_o and beta_q, Vhat the initial covariance matrix of adaptive M-H for theta, beta0 and S0 the prior for each of the beta_h, beta_o and beta_q, for which the default is the g-prior, theta0 and V0 the prior for theta.

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.

truncation_time

a vector of left-trucation times with length n.

subject.num

a vector of suject id numbers when time dependent covariates are considered. For example, for subject 1 time dependent covariates are recorded over [0,1), [1,3), and for subject 2 covariates are recorded over [0,2), [2,3), [3,4). Suppose we only have two subjects, i.e. n=2. In this case, we save the data in the long format, set truncation_time=c(0,1,0,2,3) and subject.num=c(1,1,2,2,2).

InitParamMCMC

flag to indicate wheter an initial MCMC will be run based on the centering parametric model, where TRUE indicates yes.

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; use names to find out what they are.

References

In preparation.

Examples

Run this code

#################################################################
# A simulated data based on PH_PO_AFT super model
#################################################################
rm(list=ls())
library(coda)
library(survival)
library(spBayesSurv)

## True coeffs
betaT_h = c(1, 1);
betaT_o = c(0, 0);
betaT_q = c(1, 1);
## 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)
}
h0oft = function(t) f0oft(t)/S0oft(t);
## The Survival function:
Sioft = function(t,x){
  xibeta_h = sum(x*betaT_h);
  xibeta_o = sum(x*betaT_o);
  xibeta_q = sum(x*betaT_q);
  (1+exp(xibeta_o-xibeta_h+xibeta_q)*
     (1/S0oft(exp(xibeta_q)*t)-1))^(-exp(xibeta_h-xibeta_q));
}
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
### true plots
tt=seq(1e-10, 4, 0.02);
xpred1 = c(0,0);
xpred2 = c(0,1);
plot(tt, Sioft(tt, xpred1), "l", ylim=c(0,1));
lines(tt, Sioft(tt, xpred2), "l");

##-------------Generate data-------------------##
## generate x 
n = 80; 
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 -------------###
t1=tT;t2=tT;
Centime = runif(n, 2, 6);
delta = (tT<=Centime) +0 ; length(which(delta==0))/n;
rcen = which(delta==0);
t1[rcen] = Centime[rcen];
t2[rcen] = NA;
## make a data frame
d = data.frame(t1=t1, t2=t2, x1=x1, x2=x2, delta=delta, tT=tT); table(d$delta)/n;

##-------------Fit the model-------------------##
# MCMC parameters
nburn=200; nsave=500; nskip=0; niter = nburn+nsave
mcmc=list(nburn=nburn, nsave=nsave, nskip=nskip, ndisplay=1000);
prior = list(maxL=15, a0=1, b0=1, M=10, q=.9);
state <- list(cpar=1);
ptm<-proc.time()
res1 = SuperSurvRegBayes(formula = Surv(t1, t2, type="interval2")~x1+x2, data=d, 
                          prior=prior, mcmc=mcmc, state=state, dist="lognormal");
sfit=summary(res1); sfit;
systime1=proc.time()-ptm; systime1;
par(mfrow = c(3,2))
traceplot(mcmc(res1$beta_h[1,]), main="beta_h for x1");
traceplot(mcmc(res1$beta_h[2,]), main="beta_h for x2");
traceplot(mcmc(res1$beta_o[1,]), main="beta_o for x1");
traceplot(mcmc(res1$beta_o[2,]), main="beta_o for x2");
traceplot(mcmc(res1$beta_q[1,]), main="beta_q for x1");
traceplot(mcmc(res1$beta_q[2,]), main="beta_q for x2");

####################################################################
## Get curves
####################################################################
wide=0.2;
tgrid = seq(1e-10,4,wide);
ngrid = length(tgrid);
xpred = rbind(c(0,0), c(0,1)); 
estimates=plot(res1, xpred=xpred, tgrid=tgrid);
## plots
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$tgrid, estimates$Shat[,2], lty=2, lwd=3)