Background: Conventional decomposition analysis identifies contributions from differences in covariates in total between-population difference, but does not address the question of the historical roots of the differences. To close this gap, the contour decomposition method was proposed. Since 2017, when it was published, this method has been successfully applied in several papers. Nevertheless, it has an important limitation: causes of death cannot be included in the analyses. Objective: Conventional decomposition analysis provides insight into the reasons for a difference in an aggregate index. It can be either the difference between two populations at a given time or a temporal change for one population. However, it does not consider the origin of this difference. Contour decomposition is the only method that does. We extend the contour decomposition method by adding one more dimension that can be used to estimate the contribution of an additional component; e.g., causes of death or educational structure. Methods: We use a step-wise replacement algorithm. Contribution: The proposed discrete method for decomposition is an extension of the earlier general algorithm of stepwise replacement and contour decomposition and permits a difference in an aggregate measure at a final time point to be split into cause-specific additive components that correspond to the initial differences in the event-rates of the measure and differences in trends in these underlying event-rates.

中文翻译：

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二维轮廓分解：按年龄和死因将死亡率差异分解为初始差异和趋势成分（作者：Dmitri Jdanov、Domantas Jasilionis、Vladimir Shkolnikov）


背景：传统的分解分析确定了协变量差异对群体间总差异的贡献，但没有解决差异的历史根源问题。为了弥补这一差距，提出了轮廓分解方法。自2017年发表以来，该方法已在多篇论文中成功应用。然而，它有一个重要的局限性：死亡原因不能包含在分析中。目标：传统的分解分析可以深入了解总体指数差异的原因。它可以是给定时间两个群体之间的差异，也可以是一个群体的时间变化。然而，它没有考虑这种差异的根源。轮廓分解是唯一能做到这一点的方法。我们通过添加一个维度来扩展轮廓分解方法，该维度可用于估计附加组件的贡献；例如，死亡原因或教育结构。方法：我们使用逐步替换算法。贡献：所提出的离散分解方法是早期逐步替换和轮廓分解的通用算法的扩展，并允许最终时间点的聚合测量的差异被分割成与初始差异相对应的特定原因的加性分量衡量的事件发生率以及这些基本事件发生率的趋势差异。