tbs.survreg.mle: MLE of the TBS Model for Failure Data

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

Description

This function performs the Maximum Likelihhod Estimation of the TBS model. The optimization is done by the function ‘optim’ (or optionally the package Rsolnp when available).

Usage

 tbs.survreg.mle(formula,dist=dist.error("all"),
                 method=c("Nelder-Mead", "BFGS", "Rsolnp", "SANN", "CG"),
                 verbose=FALSE,nstart=10,max.time=-1,seed=1234,gradient=FALSE)

Arguments

formula	A formula specification containing a Surv model with right-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.
method	a vector of numerical methods to be used in the optimization. The function try all listed methods and returns all results, together with an indication of the solution with maximal likelihood among them.
verbose	Boolean to indicate the amount of output during the execution of the optimization.
nstart	Number of feasible initial points to guess when performing the optimization.
max.time	Maximum time (in minutes) to run the optimization (<= 0 means no limit).
seed	The number that is used to initialize the seed for random number generation.
gradient	if TRUE, MLE tries to use the implemented gradient functions (usually the numerical ones are ok).

Details

This function calls numerical optimization methods to maximize the likelihood of the TBS model, according to the given error distribution, method of optimization, and formula. The formula is supposed to have a Surv object and possibility co-variates, just as the standard specification of R formulas. The optimizers are going to do their best to find high likelihood estimates, but as in most estimation methods that need a numerical optimization procedure, the obtained estimate cannot be guaranteed to be a global optimal solution, but instead is dependent on the initial guessing points, and thus on the seed of the random number generation.

Value

Either an element of class tbs.survreg.mle (with print, summary, and plot functions) or a list of them (depending whether the call of tbs.survreg.mle was made for a single distribution or a list of them). In case it is a list, additional fields named best and best.n give the name and the position of the best estimation in the list, respectively. Each element of tbs.survreg.mle has the following components:

lambda	The estimate for parameter lambda
xi	The estimate for parameter xi
beta	A vector with the estimate for parameter beta
lambda.se	The standard error for parameter lambda
xi.se	The standard error for parameter xi
beta.se	A vector with the standard error for parameter beta
log.lik	The log-likelihood at parameters par.
error.dist	The error distribution chosen.
AIC	Akaike Information Criterion.
AICc	AICc is AIC with a second order correction for small sample sizes.
BIC	Bayesian Information Criterion.
method	Numerical method used to achive the MLE.
convergence	If convergence is FALSE then it was not possible to find the MLE.
time	observed survival times.
error	error of the estimated model.
call	function evaluated.
formula	formula entered by user.
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.be,dtbs,ptbs,qtbs,rtbs.

Examples

# 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)

# MLE estimation with logistic error
formula <- survival::Surv(alloyT7987$time,alloyT7987$delta == 1) ~ 1
tbs.mle <- tbs.survreg.mle(formula,dist=dist.error("logistic"),method="Nelder-Mead",nstart=3)

# Kaplan-Meier estimation
km <- survival::survfit(formula)

# Plot survival function
plot(tbs.mle)
lines(km)

# Plot hazard function
plot(tbs.mle, plot.type="hazard")

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