Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada.
Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON, Canada.
Stat Methods Med Res. 2020 Nov;29(11):3308-3325. doi: 10.1177/0962280220925840. Epub 2020 May 29.
Due to the inevitable inter-study correlation between test sensitivity (Se) and test specificity (Sp), mostly because of threshold variability, hierarchical or bivariate random-effects models are widely used to perform a meta-analysis of diagnostic test accuracy studies. Conventionally, these models assume that the random-effects follow the bivariate normal distribution. However, the inference made using the well-established bivariate random-effects models, when outlying and influential studies are present, may lead to misleading conclusions, since outlying or influential studies can extremely influence parameter estimates due to their disproportional weight. Therefore, we developed a new robust bivariate random-effects model that accommodates outlying and influential observations and gives robust statistical inference by down-weighting the effect of outlying and influential studies. The marginal model and the Monte Carlo expectation-maximization algorithm for our proposed model have been derived. A simulation study has been carried out to validate the proposed method and compare it against the standard methods. Regardless of the parameters varied in our simulations, the proposed model produced robust point estimates of Se and Sp compared to the standard models. Moreover, our proposed model resulted in precise estimates as it yielded the narrowest confidence intervals. The proposed model also generated a similar point and interval estimates of Se and Sp as the standard models when there are no outlying and influential studies. Two published meta-analyses have also been used to illustrate the methods.
由于测试灵敏度（Se）和测试特异性（Sp）之间不可避免的相互关联，主要是由于阈值变化，广泛使用分层或双变量随机效应模型来对诊断测试准确性研究进行荟萃分析。传统上，这些模型假设随机效应遵循双变量正态分布。然而，当存在异常值和有影响力的研究时，使用成熟的双变量随机效应模型进行推断可能会导致误导性的结论，因为异常值或有影响力的研究由于其不成比例的权重，可能会对参数估计产生极大影响。因此，我们开发了一种新的稳健双变量随机效应模型，该模型可以容纳异常值和有影响力的观察值，并通过对异常值和有影响力的研究进行权重降低来提供稳健的统计推断。已经推导出了我们提出的模型的边缘模型和蒙特卡罗期望最大化算法。进行了模拟研究来验证该方法，并将其与标准方法进行比较。无论在模拟中改变哪些参数，与标准模型相比，所提出的模型都能产生稳健的 Se 和 Sp 点估计值。此外，由于我们的模型产生了最窄的置信区间，因此它能够得出精确的估计值。当没有异常值和有影响力的研究时，所提出的模型也会产生与标准模型相似的 Se 和 Sp 的点估计值和区间估计值。还使用两个已发表的荟萃分析来说明这些方法。
