Empirical likelihood confidence intervals for regression parameters of the survival rate

The survival probability of patients plays an important role in biomedical settings. Based on the Jung [(1996), 'Regression Analysis for Long-Term Survival Rate', Biometrika, 83, 227-232] regression model for survival probability, Zhao [(2005), 'Regression Analysis for Long-Term Survival Rate Via Empirical Likelihood', Journal of Nonparametric Statistics, 17, 995-1007] developed an empirical likelihood (EL) confidence region for the vector of regression parameters. However, the proposed EL method does not work for a subset of regression parameters. In this paper, we develop EL confidence regions for any subset or a linear combination of the vectors of the regression parameters under the regression model. We propose two kinds of confidence intervals for the survival rate of a patient with the given covariates. A simulation study is carried out to compare the proposed method with the normal approximation-based method and nonparametric bootstrap method. Finally, we compare the proposed procedure with the existing method using a clinical trial data set.