Modified profile likelihood estimation for the Weibull regression models in survival analysis

In this study, adjustment of profile likelihood function of parameter of interest in presence of many nuisance parameters is investigated for survival regression models. Our objective is to extend the Barndorff–Nielsen’s technique to Weibull regression models for estimation of shape parameter in presence of many nuisance and regression parameters. We conducted Monte-Carlo simulation studies and a real data analysis, all of which demonstrate and suggest that the modified profile likelihood estimators outperform the profile likelihood estimators in terms of three comparison criterion: mean squared errors, bias and standard errors.