The risk over a given time span can be calculated as one minus the exponentiated value of the negative of the integral of the incidence density function (or hazard rate function) over that time span. This relationship is widely used but, in the few instances where textbooks have presented it, the derivations of it tend to be purely mathematical. I first review the historical contexts, definitions, distinctions and links. I then offer a more intuitive heuristic approach that draws on the conceptualization of a person-year in Edmonds’ 1832 definition of the force of mortality, and on the number of replacements in a dynamic population. Similarly I show how the Nelson-Aalen risk estimator can be seen in the context of this historical conceptualization of a person-year, scaled to the experience of a dynamic population of (constant) size 1.

给定时间跨度内的风险可以计算为 1 减去该时间跨度内发生密度函数（或风险率函数）积分的负数的指数值。这种关系被广泛使用，但在教科书介绍它的少数情况下，它的推导往往是纯粹的数学。我首先回顾了历史背景、定义、区别和联系。然后，我提供了一种更直观的启发式方法，该方法借鉴了 Edmonds 1832 年对死亡率力量的定义中对人年的概念化，以及动态人口中的替代人数。同样，我展示了如何在这种人年的历史概念化的背景下看待 Nelson-Aalen 风险估计器，并根据（恒定）大小为 1 的动态人口的经验进行缩放。