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

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Description

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

Usage

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psbcFL(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, r1, r2, delta1, delta2, s

initial

The list containing the starting values of the parameters; beta.ini, lambda1Sq, lambda2Sq, sigmaSq, tauSq, h, wSq

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 β; 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
r1 the shape parameter of the gamma prior for λ_1^2
r2 the shape parameter of the gamma prior for λ_2^2
delta1 the rate parameter of the gamma prior for λ_1^2
delta2 the rate parameter of the gamma prior for λ_2^2
s the set of time partitions for specification of the cumulative baseline hazard function
beta.ini the starting values for β
lambda1Sq the starting value for λ_1^2
lambda2Sq the starting value for λ_2^2
sigmaSq the starting value for σ^2
tauSq the starting values for τ^2
h the starting values for h
wSq the starting values for w^2
numBeta the number of components in β to be updated at one iteration
beta.prop.var the variance of the proposal density for β when rw is set to "TRUE"

Value

psbcFL returns an object of class psbcFL

beta.p

posterior samples for β

h.p

posterior samples for h

tauSq.p

posterior samples for τ^2

mcmcOutcome

The list containing posterior samples for the remaining model parameters

Note

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

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## Not run: 

# generate some survival data
	
	set.seed(204542)
	
	p = 20
	n = 100
	beta.true <- c(rep(4, 10), rep(0, (p-10)))	
	
	CovX<- diag(0.1, p)
	
	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$eta0 		<- 2
	priorPara$kappa0 	<- 2
	priorPara$c0 		<- 2
	priorPara$r1		<- 0.5
	priorPara$r2		<- 0.5
	priorPara$delta1	<- 0.0001
	priorPara$delta2	<- 0.0001
	priorPara$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)

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

	initial				<- list()
	initial$beta.ini	<- rep(0.5, p)
	initial$lambda1Sq	<- 1  
	initial$lambda2Sq	<- 1  
	initial$sigmaSq		<- runif(1, 0.1, 10)
	initial$tauSq		<- rexp(p, rate = initial$lambda1Sq/2)
	initial$h			<- rgamma(priorPara$J, 1, 1)
	initial$wSq	 		<- rexp((p-1), rate = initial$lambda2Sq/2)

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

	fitFL <- psbcFL(survObj, priorPara, initial, rw=FALSE, mcmcPara, 
				num.reps, thin, chain, save)
	
## End(Not run)