tbs.survreg.be: Bayesian Estimation of the TBS Model for Survival Data

In TBSSurvival: Survival Analysis using a Transform-Both-Sides Model

Description

This function performs the Bayesian estimation of the Transform-Both-Sides (TBS) model. The priors for the parameters ‘lambda’ and ‘xi’ are uniform-exponential mixtures and, if not specified, for parameter beta is a normal with mean 5 and sd 5. The estimations are done by Metropolis-Hasting (using the function ‘metrop’ availible with the package ‘mcmc’).

Usage

  tbs.survreg.be(formula, dist=dist.error("norm"),max.time = -1, guess.beta = NULL, 
                 guess.lambda = 1, guess.xi = 1, burn = 1000, jump = 2, size = 500, 
                 scale = 0.1, prior.mean = NULL, prior.sd = NULL, seed = 1234)

Arguments

formula	A formula specification containing a Surv model with right-censored (or no censored) data as in the package survival.
dist	Error distribution; dist can be given by name ("norm", "doubexp", "t", "cauchy" or "logistic") or by dist.error.
max.time	Maximum time (in minutes) to run the optimization (<= 0 means no limit).
guess.beta	Initial value of the Markov Chain for the vector ‘beta’. Default will fill it with zeros.
guess.lambda	Initial value of the Markov Chain for the parameter ‘lambda’.
guess.xi	Initial value of the Markov Chain for the parameter ‘xi’.
burn	Burn-in: number of initial samples of the posterior not to use.
jump	Number of jumps between each sample of the posterior to avoid the problem of auto-correlation between the samples.
size	Size of final sample of the posterior.
scale	Parameter of ‘metrop’ function. Controls the acceptance rate.
prior.mean	Prior Mean for the MCMC.
prior.sd	Prior std deviation for the MCMC.
seed	The number that is used to initialize the seed for random number generation.

Details

This function performs the Bayesian estimation of the Transform-Both-Sides (TBS) model. The priors for the parameters ‘lambda’ and ‘xi’ are uniform-exponential mixtures and, if not specified, for parameter beta is a normal with mean 5 and sd 5. The estimations are done by Metropolis-Hasting (using the function ‘metrop’ availible with the package ‘mcmc’).

Value

An element of the class tbs.survreg.be, with the components:

call	function evaluated.
x	co-variable matrix used.
time	survival time.
delta	censor status.
post	posterior sample of the parameters.
lambda	posterior mean of lambda.
xi	posterior mean of xi.
beta	vector with posterior mean of beta.
lamda.sd	standard deviation for lambda.
xi.sd	standard deviation of for xi.
beta.sd	standard deviation of for beta.
lambda.HPD	95% high posterior density credal interval of lambda.
xi.HPD	95% high posterior density credal interval of xi.
beta.HPD	95% high posterior density credal interval vector of beta.
DIC	Deviance Information Criterion.
error	summary statistics for the posterior of error of TBS model.
error.dist	error distribution.
run.time	Time spent with the function.

References

Meeker, W. and Escobar, L. (1998) Statistical Methods for Reliability Data. Willey, ISBN 0-471-14328-6.

See Also

dist.error,tbs.survreg.mle,dtbs,ptbs,qtbs,rtbs.

Examples

# set.seed is used to produce the same results all times.
set.seed(1234)

# Alloy - T7987: data extracted from Meeker and Escobar (1998), pp. 131)
data(alloyT7987)
alloyT7987$time  <- as.double(alloyT7987$time)
alloyT7987$delta <- as.double(alloyT7987$delta)

# Bayesian estimation with logistic error
formula <- survival::Surv(alloyT7987$time,alloyT7987$delta == 1) ~ 1
tbs.be <- tbs.survreg.be(formula,guess.lambda=1,guess.xi=1,guess.beta=5,
                         dist=dist.error("logistic"),burn=1000,jump=10,size=500,scale=0.06)

# Kapan-Meier estimator
km <- survival::survfit(formula = survival::Surv(alloyT7987$time, alloyT7987$delta == 1) ~ 1)

# Plot survival function
plot(tbs.be,lwd=2,HPD=TRUE,HPD.alpha=0.95,col.HPD=2,lty.HPD=1,lwd.HPD=2)
lines(km)

# Plot survival function
plot(tbs.be,plot.type="hazard",lwd=2,HPD=TRUE,HPD.alpha=0.95,col.HPD=2,lty.HPD=1,lwd.HPD=2)

# Plot auto-correlation of the posterior sample
plot(tbs.be,plot.type="auto")

# Plot "time-series" of the posterior sample
plot(tbs.be,plot.type="ts")

TBSSurvival documentation built on May 2, 2019, 6:54 a.m.