Small study effects occur when smaller studies show different, often larger, treatment effects than large ones, which may threaten the validity of systematic reviews and meta-analyses. The most well-known reasons for small study effects include publication bias, outcome reporting bias and clinical heterogeneity. Methods to account for small study effects in univariate meta-analysis have been extensively studied. However, detecting small study effects in a multivariate meta-analysis setting remains an untouched research area. One of the complications is that different types of selection processes can be involved in the reporting of multivariate outcomes. For example, some studies may be completely unpublished while others may selectively report multiple outcomes. In this paper, we propose a score test as an overall test of small study effects in multivariate meta-analysis. Two detailed case studies are given to demonstrate the advantage of the proposed test over various naive applications of univariate tests in practice. Through simulation studies, the proposed test is found to retain nominal Type I error rates with considerable power in moderate sample size settings. Finally, we also evaluate the concordance between the proposed test with the naive application of univariate tests by evaluating 44 systematic reviews with multiple outcomes from the Cochrane Database.

中文翻译：

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在多变量荟萃分析中测试小型研究效果

当较小的研究显示出与大型研究不同的、通常更大的治疗效果时，就会出现小型研究效果，这可能会威胁到系统评价和荟萃分析的有效性。小规模研究影响最广为人知的原因包括发表偏倚、结果报告偏倚和临床异质性。在单变量荟萃分析中解释小型研究效应的方法已被广泛研究。然而，在多元荟萃分析环境中检测小研究效果仍然是一个未触及的研究领域。复杂情况之一是不同类型的选择过程可能涉及多变量结果的报告。例如，一些研究可能完全未发表，而另一些研究可能有选择地报告多种结果。在本文中，我们建议将分数测试作为多变量荟萃分析中小型研究效果的整体测试。给出了两个详细的案例研究，以证明所提出的测试在实践中对单变量测试的各种幼稚应用的优势。通过模拟研究，发现建议的测试在中等样本量设置下以相当大的功效保留名义 I 类错误率。最后，我们还通过评估来自 Cochrane 数据库的具有多个结果的 44 篇系统评价，来评估所提出的测试与单变量测试的幼稚应用之间的一致性。发现建议的测试在中等样本量设置下以相当大的功效保留了标称 I 类错误率。最后，我们还通过评估来自 Cochrane 数据库的具有多个结果的 44 篇系统评价，来评估所提出的测试与单变量测试的幼稚应用之间的一致性。发现建议的测试在中等样本量设置下以相当大的功效保留了标称 I 类错误率。最后，我们还通过评估来自 Cochrane 数据库的具有多个结果的 44 篇系统评价，来评估所提出的测试与单变量测试的幼稚应用之间的一致性。