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Abstract:
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This paper focuses on comparing two means and finding a confidence interval for the difference of two means with right-censored data using the empirical likelihood method combined with the i.i.d. random functions representation. Some early researchers proposed empirical likelihood-based confidence intervals for the mean difference based on right-censored data using the synthetic data approach. However, their empirical log-likelihood ratio statistic has a scaled chi-squared distribution. To avoid the estimation of the scale parameter in constructing confidence intervals, we propose an empirical likelihood method based on the i.i.d. representation of Kaplan–Meier weights involved in the empirical likelihood ratio. We obtain the standard chi-squared distribution. We also apply the adjusted empirical likelihood to improve coverage accuracy for small samples. We investigate a new empirical likelihood method, the mean empirical likelihood, within the framework of our study. Via extensive simulations, the proposed empirical likelihood confidence interval has better coverage accuracy than those from existing methods. Finally, our findings are illustrated with a real data set.
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