荟萃分析中具有单调权重函数的选择模型
Selection models with monotone weight functions in meta analysis
AI总结：
本文提出在荟萃分析选择模型中估计单调非增权重函数的非参数方法，通过正则化应对研究数量少的问题，并给出对数似然性质、检验 $p$ 值及校正选择偏倚的置信区间，配套 R 包 selectMeta 实现完全可复现。
摘要：
发表偏倚，即被纳入荟萃分析的研究并不能代表关于所关注主题的全部研究，被普遍认为是对荟萃分析结果有效性的一种威胁。显式建模发表偏倚的一种方法是使用选择模型或加权概率分布。我们采用 Dear (1992) 最初引入的非参数方法，但施加权重函数 $w$ 作为 $p$ 值的函数是单调非增的约束。由于在荟萃分析中通常只有很少的研究或“观测”，对估计问题进行正则化似乎是合理的。此外，迄今为止文献中提出的几乎所有参数权重函数实际上都是递减的。我们讨论了如何在上述模型中估计递减权重函数，并在两个众所周知的例子中说明了这一新方法。与其他方法相比，新方法可能对选择过程提供更多的洞察，并且比参数方法更灵活。文中指出了对数似然函数的一些基本性质，以及计算一个 $p$ 值来量化反对常数权重函数零假设的证据。此外，我们提供了一个近似的针对选择偏倚调整的剖面似然置信区间，用于处理效应。相应的软件和用于说明该方法的数据集以 R 包 selectMeta 的形式提供。这使得本文的结果可以完全重现。
英文摘要：
Publication bias, the fact that studies identified for inclusion in a meta analysis do not represent all studies on the topic of interest, is commonly recognized as a threat to the validity of the results of a meta analysis. One way to explicitly model publication bias is via selection models or weighted probability distributions. We adopt the nonparametric approach initially introduced by Dear (1992) but impose that the weight function $w$ is monotonely non-increasing as a function of the $p$-value. Since in meta analysis one typically only has few studies or "observations", regularization of the estimation problem seems sensible. In addition, virtually all parametric weight functions proposed so far in the literature are in fact decreasing. We discuss how to estimate a decreasing weight function in the above model and illustrate the new methodology on two well-known examples. The new approach potentially offers more insight in the selection process than other methods and is more flexible than parametric approaches. Some basic properties of the log-likelihood function and computation of a $p$-value quantifying the evidence against the null hypothesis of a constant weight function are indicated. In addition, we provide an approximate selection bias adjusted profile likelihood confidence interval for the treatment effect. The corresponding software and the datasets used to illustrate it are provided as the R package selectMeta. This enables full reproducibility of the results in this paper.
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