psbcGL {psbcGroup}

Function to Fit the Penalized Semiparametric Bayesian Cox Model with Group Lasso Prior

Description

Penalized semiparametric Bayesian Cox (PSBC) model with group lasso prior is implemented to analyze survival data with high-dimensional covariates.

Usage

psbcGL(survObj, priorPara, initial, rw=FALSE, mcmcPara, num.reps, 
		thin, chain = 1, save = 1000)

Arguments

survObj

The list containing observed data from n subjects; t, di, x

priorPara

The list containing prior parameter values; eta0, kappa0, c0, r, delta, s, groupInd

initial

The list containing the starting values of the parameters; beta.ini, lambdaSq, sigmaSq, tauSq, h

rw

When setting to "TRUE", the conventional random walk Metropolis Hastings algorithm is used. Otherwise, the mean and the variance of the proposal density is updated using the jumping rule described in Lee et al. (2011).

mcmcPara

The list containing the values of options for Metropolis-Hastings step for \beta; numBeta, beta.prop.var

num.reps

the number of iterations of the chain

thin

thinning

chain

the numeric name of chain in the case when running multiple chains.

save

frequency of storing the results in .Rdata file. For example, by setting "save = 1000", the algorithm saves the results every 1000 iterations.

Details

t	a vector of n times to the event
di	a vector of n censoring indicators for the event time (1=event occurred, 0=censored)
x	covariate matrix, n observations by p variables
eta0	scale parameter of gamma process prior for the cumulative baseline hazard, eta0 > 0
kappa0	shape parameter of gamma process prior for the cumulative baseline hazard, kappa0 > 0
c0	the confidence parameter of gamma process prior for the cumulative baseline hazard, c0 > 0
r	the shape parameter of the gamma prior for \lambda^2
delta	the rate parameter of the gamma prior for \lambda^2
s	the set of time partitions for specification of the cumulative baseline hazard function
groupInd	a vector of p group indicator for each variable
beta.ini	the starting values for \beta
lambdaSq	the starting value for \lambda^2
sigmaSq	the starting value for \sigma^2
tauSq	the starting values for \tau^2
h	the starting values for h
numBeta	the number of components in \beta to be updated at one iteration
beta.prop.var	the variance of the proposal density for \beta when rw is set to "TRUE"

Value

psbcGL returns an object of class psbcGL

beta.p

posterior samples for \beta

h.p

posterior samples for h

tauSq.p

posterior samples for \tau^2

mcmcOutcome

The list containing posterior samples for the remaining model parameters

Note

To fit the PSBC model with the ordinary Bayesian lasso prior (Lee et al., 2011), groupInd needs to be set to 1:p. If the prespecified value of save is less than that of num.reps, the results are saved as .Rdata file under the directory working directory/mcmcOutcome.

Author(s)

Kyu Ha Lee, Sounak Chakraborty, (Tony) Jianguo Sun

References

Lee, K. H., Chakraborty, S., and Sun, J. (2011). Bayesian Variable Selection in Semiparametric Proportional Hazards Model for High Dimensional Survival Data. The International Journal of Biostatistics, Volume 7, Issue 1, Pages 1-32.

Lee, K. H., Chakraborty, S., and Sun, J. (2015). Survival Prediction and Variable Selection with Simultaneous Shrinkage and Grouping Priors. Statistical Analysis and Data Mining, Volume 8, Issue 2, pages 114-127.

Examples

## Not run: 

# generate some survival data
	
	set.seed(204542)
	
	p = 20
	n = 100
	beta.true <- c(rep(4, 10), rep(0, (p-10)))	

	CovX<-matrix(0,p,p)

	for(i in 1:10){
		for(j in 1:10){
			CovX[i,j] <- 0.5^abs(i-j)
			}
		}
		
	diag(CovX) <- 1
	
	survObj 	<- list()
	survObj$x	<- apply(rmvnorm(n, sigma=CovX, method="chol"), 2, scale)
	
	pred <- as.vector(exp(rowSums(scale(survObj$x, center = FALSE, scale = 1/beta.true))))
	
	t 		<- rexp(n, rate = pred)
	cen		<- runif(n, 0, 8)      
	survObj$t 		<- pmin(t, cen)
	survObj$di 		<- as.numeric(t <= cen)

	priorPara 			<- list()
	priorPara$eta0 		<- 1
	priorPara$kappa0 	<- 1
	priorPara$c0 		<- 2
	priorPara$r			<- 0.5
	priorPara$delta		<- 0.0001
	priorPara$s			<- sort(survObj$t[survObj$di == 1])
	priorPara$s			<- c(priorPara$s, 2*max(survObj$t)
	-max(survObj$t[-which(survObj$t==max(survObj$t))]))
	priorPara$J			<- length(priorPara$s)
	priorPara$groupInd	<- c(rep(1,10),2:11)

	mcmcPara				<- list()
	mcmcPara$numBeta		<- p
	mcmcPara$beta.prop.var	<- 1

	initial				<- list()
	initial$beta.ini	<- rep(0.5, p)
	initial$lambdaSq	<- 1
	initial$sigmaSq		<- runif(1, 0.1, 10)
	initial$tauSq		<- rexp(length(unique(priorPara$groupInd)),
	rate = initial$lambdaSq/2)
	initial$h			<- rgamma(priorPara$J, 1, 1)

	rw = FALSE
	num.reps = 20000
	chain = 1
	thin = 5
	save = 5

	fitGL <- psbcGL(survObj, priorPara, initial, rw=FALSE, mcmcPara, 
				num.reps, thin, chain, save)
	vs <- VS(fitGL, X=survObj$x)
				
	
## End(Not run)