Empirical-likelihood-based semiparametric inference for the treatment effect in the two-sample problem with censoring

To compare two samples of censored data, we propose a unified method of semiparametric inference for the parameter of interest when the model for one sample is parametric and that for the other is nonparametric. The parameter of interest may represent, for example, a comparison of means, or survival probabilities. The confidence interval derived from the semiparametric inference, which is based on the empirical likelihood principle, improves its counterpart constructed from the common estimating equation. The empirical likelihood ratio is shown to be asymptotically chi-squared. Simulation experiments illustrate that the method based on the empirical likelihood substantially outperforms the method based on the estimating equation. A real dataset is analysed.