MPLikelihoodWB (version 1.1)

MPLikelihoodWB-package: Modified Profile Likelihood Estimation for Weibull Shape and Regression Parameters

Description

Makes adjustment of profile likelihood function of parameter of interest in presence of many nuisance parameters under Weibull regression models. Modified profile likelihood techniue is developed by extending the Barndorff--Nielsens approach for Weibull regression models. Modified likelihood estimates are provided.

Details

A modification to profile likelihood is introduced to overcome from this type of problems. Several adjustments have been proposed to modify the profile likelihood function. In an earlier paper named Conditionality resolutions by Barndorff-Nielsen published in Biometrica (1980, 1983), the construction of ancillary statistics and the expressions for the conditional distribution of the maximum likelihood estimate, was discussed for transformation models and exponential models, with most emphasis on the latter.

The main goal is to obtain adjustment to the profile likelihood function when the parameters of interest are, firstly, shape parameter beta (or, alternatively, kappa) and secondly, regression parameter phi in Weibull regression model, even in presence of collinearity among the covariates. Note that practically correlated covariates are found in many areas of biostatistics including microarray, genetics, medical statistics. The presence of collinearity makes sometimes the estimation and inference procedure problematic and complex and the model as a whole can be found as statistically significant but the individual regression coefficients can not be (e.g. Khan and Shaw (2015)). The modified profile likelihood estimators outperform the profile likelihood estimators in terms of three statistical measures as comparison criterion: mean squared errors, bias and standard errors for weibull shape parameter.

Package:	MPLikelihoodWB
Type:	Package
Version:	1.1
Date:	2017-8-14
License:	GPL-2

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

# NOT RUN {
# For modified profile likelihood estimation
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")

# For random dataset creation
data.weibull(n = 20)
data.weibull(n = 20, shape=1.7, regco=c(2,1,3,4))
data.weibull(n = 20, shape=1.5, ncorvar=4, correlated=TRUE)

# }