In epidemiology, public health and social science, mediation analysis is often undertaken to investigate the extent to which the effect of a risk factor on an outcome of interest is mediated by other covariates. A pivotal quantity of interest in such an analysis is the mediation proportion. A common method for estimating it, termed the "difference method", compares estimates from models with and without the hypothesized mediator. However, rigorous methodology for estimation and statistical inference for this quantity has not previously been available. We formulated the problem for the Cox model and generalized linear models, and utilize a data duplication algorithm together with a generalized estimation equations approach for estimating the mediation proportion and its variance. We further considered the assumption that the same link function hold for the marginal and conditional models, a property which we term "g-linkability". We show that our approach is valid whenever g-linkability holds, exactly or approximately, and present results from an extensive simulation study to explore finite sample properties. The methodology is illustrated by an analysis of pre-menopausal breast cancer incidence in the Nurses' Health Study. User-friendly publicly available software implementing those methods can be downloaded from the last author's website (SAS) or from CRAN (R).

中文翻译：

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调解比例的估计和推断。

在流行病学，公共卫生和社会科学中，经常进行调解分析以调查其他协变量介导风险因素对目标结果的影响的程度。在这种分析中，关键的兴趣量是调解比例。一种称为“差异法”的常用估算方法，用于比较带有或不带有假定介体的模型的估算值。但是，以前尚没有用于此数量的估计和统计推断的严格方法。我们为Cox模型和广义线性模型制定了问题，并使用数据复制算法和广义估计方程方法来估计调解比例及其方差。我们进一步考虑了以下假设：边际模型和条件模型具有相同的链接函数，我们称其为“ g-可链接性”。我们证明，只要g-可链接性完全或近似成立，我们的方法都是有效的，并且可以提供广泛的模拟研究结果来探索有限的样本属性。护士健康研究中对绝经前乳腺癌发病率的分析说明了该方法。可以从最后作者的网站（SAS）或从CRAN（R）下载实现这些方法的用户友好型公共可用软件。并提供了广泛的模拟研究结果，以探索有限的样本属性。护士健康研究中对绝经前乳腺癌发病率的分析说明了该方法。可以从最后作者的网站（SAS）或CRAN（R）下载实现这些方法的用户友好的公共可用软件。并提供了广泛的模拟研究结果，以探索有限的样本属性。护士健康研究中对绝经前乳腺癌发病率的分析说明了该方法。可以从最后作者的网站（SAS）或CRAN（R）下载实现这些方法的用户友好的公共可用软件。