mplik.wb.bi: Modified profile likelihood function of Weibull regression parameters

Description

Modified profile likelihood function of Weibull regression parameters. The function considers one regression parameter at a time as parameter of interest and remaining parameters as nuisance parameters. Standard optimization procedures are required to find the estimate of certain regression parameter at a time.

Usage

mplik.wb.bi(par, Y, X, delta, whc)

Arguments

par

Initial value of parameters to be estimated by optimization

Weibull distributed failure times

covariate matrix

delta

Censoring status, coded as 0(censored observation) and 1(uncersored observation) binary integer variable

whc

Set position of regression parameter of interest corresponding predefined covariate matrix. It will take integer value from 1 to number of regression parameters.

Value

Negative log likelihood of the function at given value of parameters and data. Optimization of this function will produce maximum likelihood estimate of regression parameter of Extreme value distribution. Transformation will be required to obtain estimate of Weibull regression 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 (2016). Variable selection for survival data with a class of adaptive elastic net techniques. Statistics and Computing, 26(3): 725-741.

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))

mplik.wb.bi(par=c(1,1,1,1,1,1),Y=dat$ftime,X=model.matrix(ftime~x1+x2+x3+x4,data=dat),
delta=dat$delta,whc=2)
# }