Hierarchical models are recommended for meta-analyzing diagnostic test accuracy (DTA) studies. The bivariate random-effects model is currently widely used to synthesize a pair of test sensitivity and specificity using logit transformation across studies. This model assumes a bivariate normal distribution for the random-effects. However, this assumption is restrictive and can be violated. When the assumption fails, inferences could be misleading. In this paper, we extended the current bivariate random-effects model by assuming a flexible bivariate skew-normal distribution for the random-effects in order to robustly model logit sensitivities and logit specificities. The marginal distribution of the proposed model is analytically derived so that parameter estimation can be performed using standard likelihood methods. The method of weighted-average is adopted to estimate the overall logit-transformed sensitivity and specificity. An extensive simulation study is carried out to investigate the performance of the proposed model compared to other standard models. Overall, the proposed model performs better in terms of confidence interval width of the average logit-transformed sensitivity and specificity compared to the standard bivariate linear mixed model and bivariate generalized linear mixed model. Simulations have also shown that the proposed model performed better than the well-established bivariate linear mixed model in terms of bias and comparable with regards to the root mean squared error (RMSE) of the between-study (co)variances. The proposed method is also illustrated using a published meta-analysis data.

中文翻译：

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用于诊断测试准确性 (DTA) 研究荟萃分析的偏正态随机效应模型

建议使用分层模型对诊断测试准确性 (DTA) 研究进行元分析。双变量随机效应模型目前被广泛用于使用跨研究的 logit 变换来合成一对测试灵敏度和特异性。该模型假设随机效应呈二元正态分布。然而，这个假设是有限制的，可能会被违反。当假设失败时，推论可能会产生误导。在本文中，我们通过为随机效应假设灵活的双变量偏态正态分布来扩展当前的双变量随机效应模型，以便对 logit 敏感性和 logit 特异性进行稳健建模。所提出模型的边际分布是通过分析导出的，因此可以使用标准似然方法进行参数估计。采用加权平均的方法来估计整体logit变换的敏感性和特异性。进行了广泛的模拟研究，以研究所提出的模型与其他标准模型相比的性能。总体而言，与标准双变量线性混合模型和双变量广义线性混合模型相比，所提出的模型在平均对数转换敏感性和特异性的置信区间宽度方面表现更好。模拟还表明，所提出的模型在偏差方面比完善的双变量线性混合模型表现更好，并且在研究间（协）方差的均方根误差 (RMSE) 方面具有可比性。还使用已发布的荟萃分析数据说明了所提出的方法。