Traditional meta-analysis assumes that the effect sizes estimated in individual studies follow a Gaussian distribution. However, this distributional assumption is not always satisfied in practice, leading to potentially biased results. In the situation when the number of studies, denoted as K, is large, the cumulative Gaussian approximation errors from each study could make the final estimation unreliable. In the situation when K is small, it is not realistic to assume the random-effect follows Gaussian distribution. In this paper, we present a novel empirical likelihood method for combining confidence intervals under the meta-analysis framework. This method is free of the Gaussian assumption in effect size estimates from individual studies and from the random-effects. We establish the large-sample properties of the non-parametric estimator, and introduce a criterion governing the relationship between the number of studies, K, and the sample size of each study, n_i. Our methodology supersedes conventional meta-analysis techniques in both theoretical robustness and computational efficiency. We assess the performance of our proposed methods using simulation studies, and apply our proposed methods to two examples.

翻译：传统元分析假设各独立研究中估计的效应量服从高斯分布。然而，这一分布假设在实践中并不总能得到满足，可能导致结果产生偏差。当研究数量K较大时，每项研究累积的高斯近似误差可能使最终估计不可靠；当K较小时，假设随机效应服从高斯分布也不现实。本文提出一种新颖的经验似然方法，用于在元分析框架下合并置信区间。该方法无需对独立研究的效应量估计及随机效应做出高斯分布假设。我们确立了非参数估计量的大样本性质，并引入了一个控制研究数量K与每项研究样本量n_i之间关系的准则。本方法在理论稳健性和计算效率上均超越传统元分析技术。我们通过模拟研究评估所提方法的性能，并将所提方法应用于两个实例。