Jackknife empirical likelihood for the difference of two volumes under ROC surfaces

Novel empirical likelihood inference for the mean difference with right-censored data

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 independent and identically distributed random functions representation. In the literature, some early researchers proposed empirical link-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 independent and identically distributed 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. In addition, we investigate a new empirical likelihood method, the mean empirical likelihood, within the framework of our study. The performances of all the empirical likelihood methods are compared via extensive simulations. The proposed empirical likelihood-based confidence interval has better coverage accuracy than those from existing methods. Finally, our findings are illustrated with a real data set.

Jackknife empirical likelihood confidence intervals for assessing heterogeneity in meta-analysis of rare binary event data

In meta-analysis, the heterogeneity of effect sizes across component studies is typically described by a variance parameter in a random-effects (Re) model. In the literature, methods for constructing confidence intervals (CIs) for the parameter often assume that study-level effect sizes are normally distributed. However, this assumption might be violated in practice, especially in meta-analysis of rare binary events. We propose to use jackknife empirical likelihood (JEL), a nonparametric approach that uses jackknife pseudo-values, to construct CIs for the heterogeneity parameter. To compute jackknife pseudo-values, we employ a moment-based estimator and consider two commonly used weighing schemes (i.e., equal and inverse variance weights). We prove that with each scheme, the resulting log empirical likelihood ratio follows a chi-square distribution asymptotically. We further examine the performance of the proposed JEL methods and compare them with existing CIs through simulation studies and data examples that focus on data of rare binary events. Our numerical results suggest that the JEL method with equal weights compares favorably to alternatives, especially when (observed) effect sizes are non-normal and the number of component studies is large. Thus, it is worth serious consideration in statistical inference.