TBSSurvival (version 1.3)

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

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 (

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.

Value

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

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').

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")