Mprofile.wb: Modified profile likelihood estimation of Weibull shape and regression parameter

Description

Modified profile likelihood estimation of Weibull shape and regression parameter. The methodology was addopted from 'Conditionality resolutions' which is actually "the construction of ancillary statistics and expressions for the conditional distribution of the maximum likelihood estimate of a statistical model". The result will produce less bias with minimum mean square error; at least for Weibull shape parameter. Performances of profile and modified profile likelihood estimation are differentiable when sample size is reasonably small.

Usage

Mprofile.wb(formula, censor, data, method = "BFGS", initial = 1)

Arguments

formula

an object of class "formula".

censor

censoring status, coded as 0(censored observation) and 1(uncersored observation) binary integer variable in the data frame.

data

data frame of weibull distributed failure time, covariates and censoring variable.

method

method under which optimization is performed. Other methods are "Nelder-Mead", "CG", "L-BFGS-B", "SANN", and "Brent".

initial

Initial values of the parameters at which likelihood function will be optimized. Default value is 1 for all parameters. To change initial values input a vector of numeric values with length of number of parameters to be optimized. First initial value is attributed for shape parameter. For example, use vector c(2,3,2,3,4) as initial value for shape and four regression parameters.

Value

The function is a list with atleast the following component:

Formula

an object of class "formula"

Coefficients

estimates of the regresion parameters

Scale

estimate of scale parameter

References

Barndorff-Nielsen (1980). Conditionality resolutions. Biometrika, 67(2) : 293-310.

Barndorff-Nielsen (1983). On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70(2) : 343-365.

Khan M. H. R. and Shaw J. E. H (2015). Variable selection for survival data with a class of adaptive elastic net techniques. Statistics and Computing, DOI: 10.1007/s11222-015-9555-8.

Islam, M. M., Khan, M. H. R. and Hawlader T. (2015). Modified profile likelihood estimation for the weibull regression models in survival analysis. Submitted.

Examples

Run this code

# NOT RUN {
dat <- data.weibull(n = 40, shape=2, regco=c(2,1.5,3,2.5))

Mprofile.wb(formula=ftime~x1+x2+x3+x4,censor="delta",data=dat)

survreg(Surv(ftime,delta)~x1+x2+x3+x4,data=dat,dist="weibull")
# }