Background: The loss of kin by death has medical, psychological, and social effects on other members of a kinship network. Recent formal demographic models can account for deaths of kin, but not causes of those deaths. Objective: Our objective is to extend the matrix kinship model to analyze losses of any type of kin, at any age at death, due to any cause of death, at any age of a Focal individual. Methods: Given age-specific schedules of risk due to each cause, the projection matrix is enlarged to include multiple absorbing states representing the age at death and the cause of death of kin at each age of Focal. The fertility matrix is enlarged to include births by living kin and to exclude births by dead kin. Results: The model provides deaths experienced at each age, and accumulated up to each age, of Focal, by cause of death and age at death. Causes of death are competing risks, per-mitting the study of how the elimination of one cause displaces bereavement across kin types and age groups of the bereaved. As an example, we analyze kin death experiences attributable to each of the six leading causes of death in the US Non-Hispanic White female population. Contribution: Studies of the death of kin and bereavement of survivors can now take into account di-verse causes of death, each with its own age schedule of risks. These results may help understand how different causes of death influence kinship structures and the experience of bereavement among surviving kin.

中文翻译：

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亲属关系的正式人口统计学 V：亲属丧失、丧亲之痛和死亡原因（作者：Hal Caswell、Rachel Margolis、Ashton Verdery）

背景：因死亡而失去亲人会对亲属网络的其他成员产生医学、心理和社会影响。最近的正式人口模型可以解释亲属的死亡，但不能解释这些死亡的原因。目标：我们的目标是扩展矩阵亲属关系模型，以分析任何类型的亲属、任何死亡年龄、任何死亡原因、任何年龄的 Focal 个体的损失。方法：给定每个原因导致的特定年龄的风险表，将投影矩阵放大以包括多个吸收状态，这些吸收状态代表死亡年龄和每个 Focal 年龄的亲属死亡原因。生育率矩阵扩大到包括在世亲属的生育情况并排除已故亲属的生育情况。结果：该模型按死亡原因和死亡年龄提供了 Focal 在每个年龄经历的死亡以及累积到每个年龄的死亡。死因是相互竞争的风险，因此可以研究消除一种死因如何在不同亲属类型和死者年龄组中取代丧亲之痛。例如，我们分析了美国非西班牙裔白人女性人口中六大主要死亡原因中每一个的亲属死亡经历。贡献：对亲属死亡和幸存者丧亲之痛的研究现在可以考虑多种死因，每种死因都有自己的年龄风险表。这些结果可能有助于理解不同的死亡原因如何影响亲属关系结构以及幸存亲属的丧亲经历。